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Question
The expression cos2(A – B) + cos2 B – 2 cos(A – B) cos A cos B is ______.
Options
dependent on B
dependent on A and B
dependent on A
independent of A and B
MCQ
Fill in the Blanks
Solution
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.
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