Question

if alpha and beta are supplementary angles then sin²alpha + cos²beta=

Answer 1

Given alpha and beta are supplementary angles
Alpha+beta =180°
Beta =180°-alpha

sin^2 (alpha) + cos^2( beta)
=sin^2 (alpha)+ cos^2 (180°-alpha)
=sin^2 (alpha) +cos^2 (alpha)
=1

Answer 2

Concept:

Supplementary angles are those whos sum is 180

$sin^{2}x+cos^{2}x=1$

Given:

alpha and beta are supplementary angles

$alpha+ beta= 180$

To find:

$sin^{2} alpha + cos^{2} beta$

Solution:

In this question, it is given to us that alpha and beta are supplementary angles, that is, $alpha+ beta= 180$

Also, an equation is given to us which we have to solve.

$sin^{2} alpha + cos^{2} beta$

So, now we know that the sum of alpha and beta is 180 so we can write beta as $180-alpha$

Then our equation becomes, $sin^{2} alpha + cos^{2} (180-alpha)$

We also know that $cos(180-x)=cosx$

So we get, $sin^{2} alpha + cos^{2} alpha$

And, since $sin^{2}x+cos^{2}x=1$

so we get, $sin^{2} alpha+cos^{2} alpha=1$

Hence, the required answer is 1.

#SPJ2