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

If $a sin space x plus b cos space left parenthesis x plus theta right parenthesis plus b cos space left parenthesis x minus theta right parenthesis equals$ d then the minimum value of $vertical line cos space theta vertical line$ is equal to (where is variable)

$\frac{1}{2 | b |} \sqrt{d^{2} - a^{2}}$
$\frac{1}{2 | a |} \sqrt{d^{2} - a^{2}}$
$\frac{1}{2 | d |} \sqrt{d^{2} - a^{2}}$
$\frac{1}{| d |} \sqrt{d^{2} - a^{2}}$

hint Hint:

In the question we will first use the formula cos(A+B)=cosA.cosB-sinA.sinB and cos(A-B)=cosA.cosB+sinA.sinB then we will convert sin and cos in terms of tan using the formula $sin 2 A equals fraction numerator 2 tan A over denominator 1 plus tan squared A end fraction a n d space cos 2 A equals fraction numerator 1 minus tan squared A over denominator 1 plus tan squared A end fraction$ then we will make a quadratic equation assuming x in terms of tan. Then we will use the concept of D is greater than 0 to get the required result.

The correct answer is: $fraction numerator 1 over denominator 2 vertical line b vertical line end fraction square root of d squared minus a squared end root$

$a sin space x plus b cos space left parenthesis x plus theta right parenthesis plus b cos space left parenthesis x minus theta right parenthesis equals d rightwards double arrow a sin x plus b open parentheses cos x space cos theta minus sin x space sin theta close parentheses plus b open parentheses cos x space cos plus sin x space sin theta close parentheses equals d rightwards double arrow a space sin x plus b cos x space cos theta minus b sin x space sin theta plus b cos x space cos plus b sin x space sin theta equals d rightwards double arrow a sin x space plus 2 b. cos x. cos theta equals d rightwards double arrow a open parentheses fraction numerator 2 tan begin display style x over 2 end style over denominator 1 plus tan squared begin display style x over 2 end style end fraction close parentheses plus 2 b. open parentheses fraction numerator 1 minus tan squared begin display style x over 2 end style over denominator 1 plus tan squared begin display style x over 2 end style end fraction close parentheses. cos theta equals d rightwards double arrow 2 a space tan x over 2 plus 2 b open parentheses 1 minus tan squared x over 2 close parentheses. cos theta equals d open parentheses 1 plus tan squared x over 2 close parentheses rightwards double arrow 2 a. tan x over 2 plus 2 b cos theta minus 2 b space tan squared x over 2 cos theta minus d minus d tan squared x over 2 equals 0 rightwards double arrow negative tan squared x over 2 open parentheses 2 b cos theta plus d close parentheses plus 2 a. tan x over 2 plus 2 b cos theta minus d equals 0 rightwards double arrow tan squared x over 2 open parentheses 2 b cos theta plus d close parentheses minus 2 a. tan x over 2 minus 2 b cos theta plus d equals 0 w e space k n o w space t h a t space space D greater or equal than 0 comma b squared minus 4 a c greater or equal than 0 open parentheses negative 2 a close parentheses squared minus 4 open parentheses 2 b cos theta plus d close parentheses open parentheses d minus 2 b cos theta close parentheses greater or equal than 0 4 a squared minus 4 open square brackets d squared minus open parentheses 2 b cos theta close parentheses squared close square brackets greater or equal than 0 4 open parentheses a squared minus d squared plus 4 b squared cos squared theta close parentheses greater or equal than 0 4 b squared cos squared theta greater or equal than d squared minus a squared cos squared theta greater or equal than fraction numerator d squared minus a squared over denominator 4 b squared end fraction open vertical bar cos theta close vertical bar greater or equal than square root of fraction numerator d squared minus a squared over denominator 4 b squared end fraction end root open vertical bar cos theta close vertical bar greater or equal than fraction numerator square root of d squared minus a squared end root over denominator 2 open vertical bar b close vertical bar end fraction S o comma space t h e space m i n i m u m space v a l u e space o f open vertical bar cos theta close vertical bar equals fraction numerator square root of d squared minus a squared end root over denominator 2 open vertical bar b close vertical bar end fraction$

Related Questions to study

$a squared plus b squared plus 2 a b cos space theta equals 1 comma c squared plus d squared plus 2 c d cos space theta equals 1$ and $a c plus b d plus left parenthesis a d plus b c right parenthesis cos space theta equals 0$ then $a squared plus c squared$ =

$a squared plus b squared plus 2 a b cos space theta equals 1 comma c squared plus d squared plus 2 c d cos space theta equals 1$ and $a c plus b d plus left parenthesis a d plus b c right parenthesis cos space theta equals 0$ then $a squared plus c squared$ =

$sin to the power of 4 space pi over 16 plus sin to the power of 4 fraction numerator 3 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 5 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 7 pi over denominator 16 end fraction$

$sin to the power of 4 space pi over 16 plus sin to the power of 4 fraction numerator 3 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 5 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 7 pi over denominator 16 end fraction$

If $cos space left parenthesis A plus B plus C right parenthesis equals cos space A cos space B cos space C comma$ then $fraction numerator 8 sin space left parenthesis B plus C right parenthesis sin space left parenthesis C plus A right parenthesis sin space left parenthesis A plus B right parenthesis over denominator sin space 2 A sin space 2 B sin space 2 C end fraction$ =

If $cos space left parenthesis A plus B plus C right parenthesis equals cos space A cos space B cos space C comma$ then $fraction numerator 8 sin space left parenthesis B plus C right parenthesis sin space left parenthesis C plus A right parenthesis sin space left parenthesis A plus B right parenthesis over denominator sin space 2 A sin space 2 B sin space 2 C end fraction$ =

parallel

The maximum value of the expression $open vertical bar square root of open parentheses sin squared space x plus 2 a squared close parentheses end root minus square root of open parentheses 2 a squared minus 1 minus cos squared space x close parentheses end root close vertical bar$
where $a$ and x are real numbers is

The maximum value of the expression $open vertical bar square root of open parentheses sin squared space x plus 2 a squared close parentheses end root minus square root of open parentheses 2 a squared minus 1 minus cos squared space x close parentheses end root close vertical bar$
where $a$ and x are real numbers is

If $tan space theta minus cot space theta equals a$ and $cos space theta minus sin space theta equals b$ then $open parentheses a squared plus 4 close parentheses open parentheses b squared minus 1 close parentheses squared$

If $tan space theta minus cot space theta equals a$ and $cos space theta minus sin space theta equals b$ then $open parentheses a squared plus 4 close parentheses open parentheses b squared minus 1 close parentheses squared$

The maximum value of $open parentheses cos space alpha subscript 1 close parentheses open parentheses cos space alpha subscript 2 close parentheses horizontal ellipsis open parentheses cos space alpha subscript n close parentheses$ under the restrictions $0 less or equal than alpha subscript 1 comma alpha subscript 2 horizontal ellipsis horizontal ellipsis alpha subscript n less or equal than pi over 2$ and $cot space alpha subscript 1 times cot space alpha subscript 2 horizontal ellipsis horizontal ellipsis cot space alpha subscript n equals 1$ is

The maximum value of $open parentheses cos space alpha subscript 1 close parentheses open parentheses cos space alpha subscript 2 close parentheses horizontal ellipsis open parentheses cos space alpha subscript n close parentheses$ under the restrictions $0 less or equal than alpha subscript 1 comma alpha subscript 2 horizontal ellipsis horizontal ellipsis alpha subscript n less or equal than pi over 2$ and $cot space alpha subscript 1 times cot space alpha subscript 2 horizontal ellipsis horizontal ellipsis cot space alpha subscript n equals 1$ is

parallel

Let $P equals left curly bracket theta colon sin space theta minus cos space theta equals square root of 2 cos space theta right curly bracket text and end text Q equals left curly bracket theta colon sin space theta plus cos space theta equals square root of 2 sin space theta right curly bracket$ be two sets. Then

Let $P equals left curly bracket theta colon sin space theta minus cos space theta equals square root of 2 cos space theta right curly bracket text and end text Q equals left curly bracket theta colon sin space theta plus cos space theta equals square root of 2 sin space theta right curly bracket$ be two sets. Then

If $0 less than alpha less than pi over 6$ then $alpha left parenthesis cosec space alpha right parenthesis$ is

If $0 less than alpha less than pi over 6$ then $alpha left parenthesis cosec space alpha right parenthesis$ is

A long cylindrical tube carries a highly polished piston and has a side opening. A tuning fork of frequency n is sounded at the sound heard by the listener charges if the piston is moves in or out. At a particular position of the piston is moved through a distance of 9 cm, the intensity of sound becomes minimum, if the speed of sound is 360 m/s, the value of n is

A long cylindrical tube carries a highly polished piston and has a side opening. A tuning fork of frequency n is sounded at the sound heard by the listener charges if the piston is moves in or out. At a particular position of the piston is moved through a distance of 9 cm, the intensity of sound becomes minimum, if the speed of sound is 360 m/s, the value of n is

physics-General

parallel

The value of $cot space fraction numerator 7 pi over denominator 16 end fraction plus 2 cot space fraction numerator 3 pi over denominator 8 end fraction plus cot space fraction numerator 15 pi over denominator 16 end fraction$

The value of $cot space fraction numerator 7 pi over denominator 16 end fraction plus 2 cot space fraction numerator 3 pi over denominator 8 end fraction plus cot space fraction numerator 15 pi over denominator 16 end fraction$

For any real $theta$ , the maximum value of $cos squared space left parenthesis cos space theta right parenthesis plus sin squared space left parenthesis sin space theta right parenthesis$ is

For any real $theta$ , the maximum value of $cos squared space left parenthesis cos space theta right parenthesis plus sin squared space left parenthesis sin space theta right parenthesis$ is

Identify A and B

Identify A and B

chemistry-General

parallel

If $square root of 2 cos space A equals cos space B plus cos cubed space B text and end text square root of 2 sin text end text A equals sin space B minus sin cubed space B$ then sin (A-B) =

If $square root of 2 cos space A equals cos space B plus cos cubed space B text and end text square root of 2 sin text end text A equals sin space B minus sin cubed space B$ then sin (A-B) =

Observer the following reactions and predict the nature of A and B

Observer the following reactions and predict the nature of A and B

chemistry-General

on ozonolysis gives

on ozonolysis gives

chemistry-General

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.