Mark the Correct alternative in the following:

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


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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