The number of solution of the equation $sin 5 x cos 3 x = sin 9 x cos 7 x$ lying in the interval $[0, \frac{π}{4}]$ is

5

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $5$
We have $sin 5 x cos 3 x = sin 9 x cos 7 x$
$2 sin 5 x cos 3 x = 2 sin 9 x cos 7 x$
$\Rightarrow sin 8 x + sin 2 x = sin 16 x + sin 2 x$
$\Rightarrow sin 8 x = 2 sin 8 x cos 8 x$
$sin 8 x = 0$ gives three solutions $0, \frac{π}{8}, \frac{π}{4}$
$cos 8 x = 0$ gives two solutions $\frac{π}{24}, \frac{5 π}{24}$

Suggest Corrections

Similar questions

sin 5 x c o s 3 x = sin 6 x cos 2 x

[0, π]

tan x + sec x = 2 cos x

π

The number of solutions of equation, sin5x cos 3x = sin 6x cos 2x, in the

interval [0, $π$ ] are

{sin}^{- 1} (4 {sin}^{2} θ + sin θ) + {cos}^{- 1} (6 sin θ - 1) = \frac{π}{2}

[0, 5 π],

sin 5 x cos 3 x = sin 6 x cos 2 x, x \in [0, π]

Join BYJU'S Learning Program