Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

The equation $2 sin x over 2 cos squared x minus 2 sin x over 2 sin squared x equals cos squared x minus sin squared x$ has a root for which the false statement is

sin2x=1
$\cos x = \frac{1}{2}$
$\cos 2 x = - \frac{1}{2}$
cosx=1

hint Hint:

In this question first we will rearrange the given expression then we will use the Half-Angle formula $cos open parentheses 2 x close parentheses equals cos squared open parentheses x close parentheses minus sin squared open parentheses x close parentheses$ .

The correct answer is: cosx=1

In this question we have to find the roots of the equation $2 sin open parentheses x over 2 close parentheses cos squared open parentheses x close parentheses space minus space 2 sin open parentheses x over 2 close parentheses sin squared open parentheses x close parentheses space equals space cos squared open parentheses x close parentheses minus sin squared open parentheses x close parentheses$

=> $2 sin open parentheses x over 2 close parentheses left parenthesis cos squared open parentheses x close parentheses minus sin squared open parentheses x close parentheses right parenthesis space equals space cos squared open parentheses x close parentheses minus sin squared open parentheses x close parentheses$
By using Half- Angle formula
$cos open parentheses 2 x close parentheses equals cos squared open parentheses x close parentheses minus sin squared open parentheses x close parentheses$
=> $2 sin open parentheses x over 2 close parentheses cos open parentheses 2 x close parentheses space equals space cos open parentheses 2 x close parentheses$
=> $left parenthesis 2 sin open parentheses x over 2 close parentheses minus 1 right parenthesis cos open parentheses 2 x close parentheses space equals space 0$
Hence $cos open parentheses 2 x close parentheses equals 0$ or $sin open parentheses x over 2 close parentheses equals 1 half$
Hence $x equals fraction numerator n pi over denominator 2 end fraction plus pi over 4$ or $x equals 2 n pi plus left parenthesis negative 1 right parenthesis to the power of n fraction numerator pi over denominator 3 end fraction comma k epsilon I$
We can see that $cos open parentheses x close parentheses equals 1$ does not satisfy the condition.

Related Questions to study

If $0 less than theta comma ϕ less than pi divided by 2 text and end text x equals sum from n equals 0 to straight infinity of sin to the power of 2 n end exponent invisible function application theta comma y equals sum from n equals 0 to straight infinity of cos to the power of 2 n end exponent invisible function application ϕ subscript text and end text end subscript straight z equals sum from n equals 0 to straight infinity of cos to the power of straight n invisible function application left parenthesis theta plus ϕ right parenthesis cos to the power of straight n invisible function application left parenthesis theta minus ϕ right parenthesis$ then

If $0 less than theta comma ϕ less than pi divided by 2 text and end text x equals sum from n equals 0 to straight infinity of sin to the power of 2 n end exponent invisible function application theta comma y equals sum from n equals 0 to straight infinity of cos to the power of 2 n end exponent invisible function application ϕ subscript text and end text end subscript straight z equals sum from n equals 0 to straight infinity of cos to the power of straight n invisible function application left parenthesis theta plus ϕ right parenthesis cos to the power of straight n invisible function application left parenthesis theta minus ϕ right parenthesis$ then

if $2 tan space A plus c o t space A equals tan space B$ then $c o t space A plus 2 tan space left parenthesis A minus B right parenthesis equals$

if $2 tan space A plus c o t space A equals tan space B$ then $c o t space A plus 2 tan space left parenthesis A minus B right parenthesis equals$

$text If end text fraction numerator cos begin display style text end text end style A over denominator cos begin display style text end text end style B end fraction equals n text and end text fraction numerator sin begin display style text end text end style A over denominator sin begin display style text end text end style B end fraction equals m text then end text open parentheses m squared minus n squared close parentheses sin squared text end text B equals$

$text If end text fraction numerator cos begin display style text end text end style A over denominator cos begin display style text end text end style B end fraction equals n text and end text fraction numerator sin begin display style text end text end style A over denominator sin begin display style text end text end style B end fraction equals m text then end text open parentheses m squared minus n squared close parentheses sin squared text end text B equals$

parallel

Find the projection of the vector $a with rightwards arrow on top equals 2 i with hat on top plus 3 j with hat on top plus 2 k with hat on top$ on the vector $stack b with rightwards arrow on top equals$ $i with ˆ on top plus 2 j with ˆ on top plus k with ˆ on top.$

Find the projection of the vector $a with rightwards arrow on top equals 2 i with hat on top plus 3 j with hat on top plus 2 k with hat on top$ on the vector $stack b with rightwards arrow on top equals$ $i with ˆ on top plus 2 j with ˆ on top plus k with ˆ on top.$

Let $stack a with ‾ on top equals 2 stack i with ˆ on top plus 3 stack j with ˆ on top minus 6 stack k with ˆ on top comma stack b with rightwards arrow on top equals 2 stack i with ˆ on top minus 3 stack j with ˆ on top plus 6 stack k with ˆ on top$ and $stack c with ‾ on top equals negative 2 stack i with ˆ on top plus 3 stack j with ˆ on top plus 6 stack k with ˆ on top times$ let $stack a with rightwards arrow on top subscript 1 end subscript$ be projection of $stack a with rightwards arrow on top$ on $stack b with rightwards arrow on top$ and $stack a with rightwards arrow on top subscript 2 end subscript$ be the projection of $stack a with rightwards arrow on top subscript 1 end subscript$ on $stack c with rightwards arrow on top$ . Then $stack a with rightwards arrow on top subscript 2 end subscript equals$

Let $stack a with ‾ on top equals 2 stack i with ˆ on top plus 3 stack j with ˆ on top minus 6 stack k with ˆ on top comma stack b with rightwards arrow on top equals 2 stack i with ˆ on top minus 3 stack j with ˆ on top plus 6 stack k with ˆ on top$ and $stack c with ‾ on top equals negative 2 stack i with ˆ on top plus 3 stack j with ˆ on top plus 6 stack k with ˆ on top times$ let $stack a with rightwards arrow on top subscript 1 end subscript$ be projection of $stack a with rightwards arrow on top$ on $stack b with rightwards arrow on top$ and $stack a with rightwards arrow on top subscript 2 end subscript$ be the projection of $stack a with rightwards arrow on top subscript 1 end subscript$ on $stack c with rightwards arrow on top$ . Then $stack a with rightwards arrow on top subscript 2 end subscript equals$

$text If end text sin text end text A plus sin space B equals square root of 3 left parenthesis cos space B minus cos space A right parenthesis$ then $sin space 3 A plus sin space 3 B equals$

$text If end text sin text end text A plus sin space B equals square root of 3 left parenthesis cos space B minus cos space A right parenthesis$ then $sin space 3 A plus sin space 3 B equals$

parallel

$s i n squared space alpha plus c o s squared space left parenthesis alpha plus beta right parenthesis plus 2 s i n space alpha s i n space beta c o s space left parenthesis alpha plus beta right parenthesis equals$

$s i n squared space alpha plus c o s squared space left parenthesis alpha plus beta right parenthesis plus 2 s i n space alpha s i n space beta c o s space left parenthesis alpha plus beta right parenthesis equals$

$text If end text sin text end text x cos space y equals 1 fourth$ and $3 tan space x equals 4 tan space y$ then $sin space left parenthesis x minus y right parenthesis equals$

$text If end text sin text end text x cos space y equals 1 fourth$ and $3 tan space x equals 4 tan space y$ then $sin space left parenthesis x minus y right parenthesis equals$

$c o t space A c o t space B equals 2 comma cos space left parenthesis A plus B right parenthesis equals 3 divided by 5 rightwards double arrow sin space A sin space B equals$

$c o t space A c o t space B equals 2 comma cos space left parenthesis A plus B right parenthesis equals 3 divided by 5 rightwards double arrow sin space A sin space B equals$

parallel

$text If end text x cos space theta equals y cos space open parentheses theta plus fraction numerator 2 pi over denominator 3 end fraction close parentheses equals z cos space open parentheses theta plus fraction numerator 4 pi over denominator 3 end fraction close parentheses$ then the value of $1 over x plus 1 over y plus 1 over z equals$

$text If end text x cos space theta equals y cos space open parentheses theta plus fraction numerator 2 pi over denominator 3 end fraction close parentheses equals z cos space open parentheses theta plus fraction numerator 4 pi over denominator 3 end fraction close parentheses$ then the value of $1 over x plus 1 over y plus 1 over z equals$

$text If end text 0 less than alpha comma beta less than pi over 4 comma cos space left parenthesis alpha plus beta right parenthesis equals 4 over 5 comma sin space left parenthesis alpha minus beta right parenthesis equals 5 over 13 text then end text tan text end text 2 alpha equals$

$text If end text 0 less than alpha comma beta less than pi over 4 comma cos space left parenthesis alpha plus beta right parenthesis equals 4 over 5 comma sin space left parenthesis alpha minus beta right parenthesis equals 5 over 13 text then end text tan text end text 2 alpha equals$

if $tan space left parenthesis A minus B right parenthesis equals 7 divided by 24 comma tan space A equals 4 divided by 3$ where A, B acute, then A+B=

if $tan space left parenthesis A minus B right parenthesis equals 7 divided by 24 comma tan space A equals 4 divided by 3$ where A, B acute, then A+B=

parallel

$text If end text cos space A equals 5 over 13 comma tan space B equals fraction numerator negative 15 over denominator 8 end fraction comma negative 270 to the power of ring operator less than straight A less than 360 to the power of ring operator comma 90 to the power of ring operator less than straight B less than 180 to the power of ring operator$ , then the quadrant to which A+B belongs is

$text If end text cos space A equals 5 over 13 comma tan space B equals fraction numerator negative 15 over denominator 8 end fraction comma negative 270 to the power of ring operator less than straight A less than 360 to the power of ring operator comma 90 to the power of ring operator less than straight B less than 180 to the power of ring operator$ , then the quadrant to which A+B belongs is

In a $triangle A B C comma fraction numerator t a n invisible function application B over denominator t a n invisible function application C end fraction equals 2 over 3$ and $t a n invisible function application A t a n invisible function application B t a n invisible function application C equals 6$ then the value(s) satisfy the equation

In a $triangle A B C comma fraction numerator t a n invisible function application B over denominator t a n invisible function application C end fraction equals 2 over 3$ and $t a n invisible function application A t a n invisible function application B t a n invisible function application C equals 6$ then the value(s) satisfy the equation

$t a n space 40 to the power of ring operator plus t a n space 80 to the power of ring operator minus √ 3 t a n space 40 to the power of ring operator t a n space 80 to the power of ring operator equals$

$t a n space 40 to the power of ring operator plus t a n space 80 to the power of ring operator minus √ 3 t a n space 40 to the power of ring operator t a n space 80 to the power of ring operator equals$

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.