The general solution of $s i n x + s i n 5 x = s i n 2 x + s i n 4 x$ is:

2 n π

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n π

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n π / 3

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2 n π / 3

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Solution

The correct option is C $n π / 3$
$s i n x + s i n 5 x = s i n 2 x + s i n 4 x$
$\Rightarrow 2 s i n 3 x c o s 2 x = 2 s i n 3 x c o s x$
$\Rightarrow 2 s i n 3 x [c o s 2 x - c o s x] = 0$
$\Rightarrow 2 s i n 3 x (2 c o s x + 1) (c o s x - 1) = 0$
Hence $s i n 3 x = 0$ or $2 c o s x + 1 = 0$ or $c o s x = 1$
The generalised solution is option C

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