Question

The expression cos²(A – B) + cos² B – 2 cos(A – B) cos A cos B is ______.

विकल्प

• dependent on B

• dependent on A and B

• dependent on A

• independent of A and B

Answer 1

The expression cos²(A – B) + cos² B – 2 cos(A – B) cos A cos B is dependent on A.

Explanation:

cos²(A – B) + cos² B – 2 cos(A – B) cos A cos B

= cos²(A – B) + cos² B – cos(A – B) {cos(A – B) + cos(A + B)}

= cos² B – cos(A – B) cos(A + B)

= cos² B – (cos² A – sin² B)

= 1 – cos² A 

= sin² A

Hence, it depends on A.