First slide

Trigonometric equations

Question

$The general solution of \sin^{10} x + \cos^{10} x = \frac{29}{16} \cos^{4} 2 x is$

Moderate

A

$\frac{n π}{4} + \frac{π}{8}, n \in I$
B

$n π + \frac{π}{8}, n \in I$
C

$\frac{n π}{8} + \frac{π}{4}, n \in I$
D

$n π + \frac{π}{4}, n \in I$

Solution

${(S i n^{2} x)}^{5} + {(\cos^{2} x)}^{5} = \frac{29}{16} \cos^{4} 2 x$
${(\frac{1 - \cos 2 x}{2})}^{5} + {(\frac{1 + \cos 2 x}{2})}^{5} = \frac{29}{16} \cos^{4} 2 x$
put cos2x=t
${(\frac{1 - t}{2})}^{5} + {(\frac{1 + t}{2})}^{5} = \frac{29 t^{4}}{16}$
$\Rightarrow 24 t^{4} - 10 t^{2} - 1 = 0$
$By inspection, t^{2} = \frac{1}{2}$
$\cos^{2} 2 x = \frac{1}{2}$
$\frac{1 + \cos 4 x}{2} = \frac{1}{2}$
$\cos 4 x = 0$
$4 x = (2 n + 1) \frac{π}{2}$
$x = (2 n + 1) \frac{π}{8}, (n \in Z)$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App