Solve the following equations.
$cos 3 x + sin 5 x = 0.$

Open in App

Solution

$cos 3 x + cos 5 x = 0$
$cos (4 x - x) + sin (4 x + x) = 0$
$cos 4 x cos x + sin 4 x sin x + sin 4 x cos x + cos 4 x sin x = 0$
$cos x (cos 4 x + sin 4 x) + sin x (sin 4 x + cos 4 x) = 0$
$(cos x + sin x) (cos 4 x + sin 4 x) = 0$
Either, $tan x = - 1$
$x = n π - \frac{π}{4} .$
or, $tan 4 x = - 1, 4 x = n π - \frac{π}{4}, x = \frac{n π}{4} - \frac{π}{16} .$

Suggest Corrections

Similar questions

s i n 3 x + 3 s i n 4 x + s i n 5 x = 0.

cos 3 x + sin 5 x = 0

sin x - sin 2 x + sin 5 x + sin 8 x = 0.

cos x - cos 2 x + cos 3 x = 0

\cos x + \cos 2 x + \cos 3 x = 0

\cos x + \cos 3 x - \cos 2 x = 0

\sin x + \sin 5 x = \sin 3 x

\cos x \cos 2 x \cos 3 x = \frac{1}{4}

\cos x + \sin x = \cos 2 x + \sin 2 x

\sin x + \sin 2 x + \sin 3 = 0

\sin x + \sin 2 x + \sin 3 x + \sin 4 x = 0

\sin 3 x - \sin x = 4 \cos^{2} x - 2

\sin 2 x - \sin 4 x + \sin 6 x = 0

Join BYJU'S Learning Program