Question

if sin square A + cos square B is equals to 1 then find the value of Cos A + B​

Answer 1

Answer:

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Answer 2

Answer:

$\cos (A+B)=\cos 2A$                            

Step-by-step explanation:

Given : If $\sin^2 A+\cos^2 B=1$

To find : The value of $\cos (A+B)$

Solution :

$\sin^2 A+\cos^2 B=1$

We know, $\sin^2 \theta+\cos^2\theta=1$

$1-\cos^2 A+\cos^2 B=1$

$\cos^2 A-\cos^2 B=0$

$\cos^2 A=\cos^2 B$

$\cos A=\cos B$  ......(1)

Similarly,

$\sin^2 A+1-\sin^2 A=1$

$\sin^2 A-\sin^2 B=0$

$\sin^2 A=\sin^2 B$

$\sin A=\sin B$  ......(2)

Now, Write the expression as

$\cos (A+B)=\cos A\cos B-\sin A\sin B$

Substitute the values,

$\cos (A+B)=\cos A\cos A-\sin A\sin A$

$\cos (A+B)=\cos^2 A-\sin^2 A$

$\cos (A+B)=\cos 2A$