Simplify : cos (36ᵒ - A)cos (36ᵒ + A) + cos (54ᵒ - A)cos (54ᵒ + A)

Simplify : cos (36ᵒ - A)cos (36ᵒ + A) + cos (54ᵒ - A)cos…

Simplify : cos (36^o - A)cos (36^o + A) + cos (54^o - A)cos (54^o + A)

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. Cos 2A.

Given that

cos (36^o - A)cos (36^o + A) + cos (54^o - A)cos (54^o + A)

As we know

Sin (90 - A) = Cos A, then

= sin(54^o + A)cos (36^o + A) + cos (54^o + A)cos (36^o + A)

We know,

Sin (A + B) = Sin A Cos B + Cos A Sin B

= Sin (54^o + A + 36^o + A) = Sin (90 + 2A)

= Cos 2A