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

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

$2 / 5$
$1 / 5$
$4 / 5$
$3 / 5$

hint Hint:

First we will convert the term $c o t space A c o t space B$ in terms of $cos open parentheses theta close parentheses$ and $sin open parentheses theta close parentheses$ as $cot open parentheses A close parentheses cot open parentheses B close parentheses space equals space fraction numerator cos open parentheses A close parentheses cos open parentheses B close parentheses over denominator sin open parentheses A close parentheses sin open parentheses B close parentheses end fraction$ . Then we will use the formula of $cos open parentheses A plus B close parentheses space equals space cos open parentheses A close parentheses cos open parentheses B close parentheses minus sin open parentheses A close parentheses sin open parentheses B close parentheses$ to find the value
of $sin open parentheses A close parentheses sin open parentheses B close parentheses$ .

The correct answer is: $3 divided by 5$

In this question we are given expression $c o t space A c o t space B equals 2$ and $cos space left parenthesis A plus B right parenthesis equals 3 divided by 5$ and we have to find the value of $sin space A sin space B$ .
Step1: Rewriting the expression $c o t space A c o t space B$ .
We know that $cot open parentheses theta close parentheses equals fraction numerator cos open parentheses theta close parentheses over denominator sin open parentheses theta close parentheses end fraction$ . So, we can rewrite above expression as
$cot open parentheses A close parentheses cot open parentheses B close parentheses space equals space fraction numerator cos open parentheses A close parentheses cos open parentheses B close parentheses over denominator sin open parentheses A close parentheses sin open parentheses B close parentheses end fraction$
=> $fraction numerator cos open parentheses A close parentheses cos open parentheses B close parentheses over denominator sin open parentheses A close parentheses sin open parentheses B close parentheses end fraction equals space 2$
=> $cos open parentheses A close parentheses cos open parentheses B close parentheses space equals space 2 sin open parentheses A close parentheses sin open parentheses B close parentheses$
Step2: Using the formula of $cos open parentheses A plus B close parentheses space equals space cos open parentheses A close parentheses cos open parentheses B close parentheses minus sin open parentheses A close parentheses sin open parentheses B close parentheses$
$cos open parentheses A close parentheses cos open parentheses B close parentheses minus sin open parentheses A close parentheses sin open parentheses B close parentheses space equals 3 over 5$
By using the values from above we get,
$2 sin open parentheses A close parentheses sin open parentheses B close parentheses minus sin open parentheses A close parentheses sin open parentheses B close parentheses space equals 3 over 5$
=> $sin open parentheses A close parentheses sin open parentheses B close parentheses space equals 3 over 5$
So, we get the value $sin open parentheses A close parentheses sin open parentheses B close parentheses space equals 3 over 5$ .

Related Questions to study

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

$text If end text 0 less than theta less than pi over 2 text and end text 2 sin invisible function application theta equals square root of 3 cos space 10 to the power of ring operator plus sin space 10 to the power of ring operator text then end text theta equals$

$text If end text 0 less than theta less than pi over 2 text and end text 2 sin invisible function application theta equals square root of 3 cos space 10 to the power of ring operator plus sin space 10 to the power of ring operator text then end text theta equals$

$cos space left parenthesis n plus 1 right parenthesis alpha cos space left parenthesis n minus 1 right parenthesis alpha plus sin space left parenthesis n plus 1 right parenthesis alpha sin space left parenthesis n minus 1 right parenthesis alpha equals$

$cos space left parenthesis n plus 1 right parenthesis alpha cos space left parenthesis n minus 1 right parenthesis alpha plus sin space left parenthesis n plus 1 right parenthesis alpha sin space left parenthesis n minus 1 right parenthesis alpha equals$

$sin space 40 to the power of ring operator 35 cos space 19 to the power of ring operator 25 plus cos space 40 to the power of ring operator 35 to the power of ring operator sin space 19 to the power of ring operator 25 equals$

$sin space 40 to the power of ring operator 35 cos space 19 to the power of ring operator 25 plus cos space 40 to the power of ring operator 35 to the power of ring operator sin space 19 to the power of ring operator 25 equals$

parallel

Assertion A: In a right-angled triangle $s i n squared space A plus s i n squared space B plus s e c squared space C equals 2$ Reason $R colon$ if $alpha comma beta$ are complementary angles then $s i n squared space alpha plus s i n squared space beta equals 1$

Assertion A: In a right-angled triangle $s i n squared space A plus s i n squared space B plus s e c squared space C equals 2$ Reason $R colon$ if $alpha comma beta$ are complementary angles then $s i n squared space alpha plus s i n squared space beta equals 1$

AB is a line segment of length 24 cm and C is its middle point. On AB, A and CB semi-circles are described. The radius of circle which touches all these semi-circles is

AB is a line segment of length 24 cm and C is its middle point. On AB, A and CB semi-circles are described. The radius of circle which touches all these semi-circles is

in a $triangle P Q R$ $3 sin space P plus 4 cos space Q equals 6$ and $4 sin space Q plus 3 cos$ p=1 then

in a $triangle P Q R$ $3 sin space P plus 4 cos space Q equals 6$ and $4 sin space Q plus 3 cos$ p=1 then

parallel

The expression $fraction numerator tan space A over denominator 1 minus cat space A end fraction plus fraction numerator cot space A over denominator 1 minus tan space d end fraction$ can be written as

The expression $fraction numerator tan space A over denominator 1 minus cat space A end fraction plus fraction numerator cot space A over denominator 1 minus tan space d end fraction$ can be written as

if $straight f subscript straight k left parenthesis straight x right parenthesis equals 1 divided by straight k left parenthesis sin to the power of straight k space straight x plus cos to the power of straight k space straight x right parenthesis$ where $straight x element of straight R comma straight k greater or equal than 1$ then $straight f subscript 4 left parenthesis straight x right parenthesis minus straight f subscript 6 left parenthesis straight x right parenthesis equals$

if $straight f subscript straight k left parenthesis straight x right parenthesis equals 1 divided by straight k left parenthesis sin to the power of straight k space straight x plus cos to the power of straight k space straight x right parenthesis$ where $straight x element of straight R comma straight k greater or equal than 1$ then $straight f subscript 4 left parenthesis straight x right parenthesis minus straight f subscript 6 left parenthesis straight x right parenthesis equals$

Two arcs of same length of two different circles subtended angles of $25 to the power of ring operator$ and $75 to the power of ring operator$ at their centers respectively. Then the ratio of the radii of the circles is

Two arcs of same length of two different circles subtended angles of $25 to the power of ring operator$ and $75 to the power of ring operator$ at their centers respectively. Then the ratio of the radii of the circles is

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.