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Chain Rule of Differentiation

Solve the fol...

Question

Solve the following equations.
$sin x + sin 2 x + sin 3 x = cos x + cos 2 x + cos 3 x .$

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Solution

$sin x + sin 2 x + sin 3 x = cos x + cos 2 x + cos 3 x$
$2 sin 2 x cos x + sin 2 x = 2 cos 2 x cos x + cos 2 x$
$2 sin 2 x (1 + cos x) = 2 cos 2 x (1 + cos x)$
Either, $cos x = - 1, x = (2 n + 1) π .$
or, $tan 2 x = n π + \frac{π}{4}, x = \frac{n π}{2} + \frac{π}{8} .$

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The number of solution of the equation $s i n x + s i n 2 x + s i n 3 x = c o s x + c o s 2 x + c o s 3 x, 0 \leq x \leq 2 π$ is

x : sin x + sin 2 x + sin 3 x = cos x + cos 2 x + cos 3 x

0 \leq x \leq 2 π

x

0

2 π

sin x + sin 2 x + sin 3 x = cos x + cos 2 x + cos 3 x,

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