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.