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

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Solution

we know if $c o s x = c o s α, x = 2 n π \pm α$

We are given cos 12x = cos 14 x

$12 x = 2 n π \pm 14 x$
We will split this into

$12 x = 2 n π + 14 x o r 12 x = 2 n π - 14 x$

$\Rightarrow x = - n π o r 13 x = n π$

$\Rightarrow s i n x = s i n (- n π) = 0 a n d s i n (13 x) = s i n (n π) = 0$

$\Rightarrow s i n x + s i n 13 x = 0$

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