Q. 30

# Mark the Correct alternative in the following:The value of cos (36o – A) cos (36o + A) + cos(54o – A) cos (54o + A) isA.cos 2AB. sin 2AC. cos AD. 0

Given expression

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

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

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

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

= cos [(36° + A) – (36° - A)]

= cos ( 2A )

Therefore the answer is option A.

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