Question

Prove that
cos²A-sin²B=cos(A+B)cos(A-B)​

Answer 1

Step-by-step explanation:

cos(A+B) cos(A-B)

=> (cosA cosB - sinA sinB) (cosA cosB +sinA sinB)

=> cos²A cos ²B - sin²A sin²B

=> cosA (1 - sin²B) - (1 - cos²A) sin²B + cos²A sin²B

=> cos²A - sin²B

Hence proved....

Answer 2

Answer:

We can also proove it vice-versa and it is very useful Identity in competitive exams.

Proof is contained by photo given along.