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The value of cos (36° – A) cos (36° + A) + cos(54° – A) cos (54° + A) is

A. cos 2A

B. sin 2A

C. cos A

D. 0

1 Answer

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Best answer

Correct answer is A.

Given expression

cos (36° – A) cos (36° + A) + cos(54° – A) cos (54° + A)

In the above expression angle cos(54° + A) = sin[90° - (54° + A)]

And cos(54° - A) = sin[90° - (54° + A)]

[using cos θ = sin (90° - θ)]

Now substituting the same in the expression

= cos (36° – A) cos (36° + A) + sin[90°- (54°– A)] sin[90°- (54° + A)]

= cos (36° – A) cos (36° + A) + sin (36° + A) sin (36° - A)

= cos (36° + A) cos (36° – A) + sin (36° + A) sin (36° - A)

[using cos (A - B) = cos A cos B + sin A sin B]

= cos [(36° + A) – (36° - A)]

= cos (2A)

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