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Question

Find the value of sin 13x + sin x if cos 12x = cos 14 x


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Solution

we know if cosx=cosα,x=2nπ±α

We are given cos 12x = cos 14 x

12x=2nπ±14x
We will split this into

12x=2nπ+14x or 12x=2nπ14x

x=nπ or 13x=nπ

sinx=sin(nπ)=0and sin(13x)=sin(nπ)=0

sinx+sin13x=0


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