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Question

Question 5
If cos(α+β)=0, then sin(αβ) can be reduced to

(A) cosβ
(B) cos2β
(C) sinα
(D) sin2α

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Solution

The answer is (B).

Given,
cos(α+β)=0=cos90 cos90=0

α+β=90

α=90β .........(i)

Now, sin(αβ)=sin(90ββ) [substituting the value from Eq. (i)]

=sin(902β)

=cos2β sin(90θ)

sin(αβ) can be reduced to cos2β.

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