The number of solutions of the equation $sin 5 x c o s 3 x = sin 6 x cos 2 x$ in the interval $[0, π]$ are

3

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4

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5

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6

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Solution

The correct option is B $4$
$sin 5 x cos 3 x = sin 6 x . cos 2 x$
Hit & Trial :
$x = 0$ , $x = π$ , $x = \frac{π}{2}$
(satisfy given eq.) in $[0, π]$
Also, $x = \frac{π}{6}$ ,
$(O R)$
$s i n x c o s y = \frac{sin (x + y) + sin (x - y)}{2}$
Now,
$\frac{1}{2} [sin 8 x + sin 2 x] = \frac{1}{2} [sin 8 x + sin 4 x]$
$\Rightarrow sin 2 x = sin 4 x$
$\Rightarrow x = 0, \frac{π}{6}, \frac{π}{2}, π$
( $4$ solutions)

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