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Question

Question 2
Write ‘True’ or ‘False’ and justify your answer in each of the following:
The value of the expression (cos2 23sin2 67) is positive.

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Solution

The statement is false.

As, 67 and 23 are complementary angles,

so,
cos2 23sin2 67=(cos 23sin 67)(cos 23+sin 67)

(a2b2)=(ab)(a+b)

=cos 23sin(9023)(cos 23+sin 67)

=(cos 23cos 23)(cos 23+sin 67) sin(90θ)=cosθ

=0

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