First slide

Multiple and sub- multiple Angles

Question

Let $f (θ) = \cos θ \cos 2 θ \cos 4 θ \cos 7 θ$ , then $f (π / 15)$ is equal to

Moderate

A

$\frac{1}{4}$
B

$\frac{1}{8}$
C

$\frac{1}{16}$
D

$\frac{1}{32}$

Solution

$\begin{array}{l} f (θ) = \frac{1}{2 \sin θ} (2 \sin θ \cos θ) \cos 2 θ \cos 4 θ \cos 7 θ \\ = \frac{1}{2 \times 2 \sin θ} (2 \sin 2 θ \cos 2 θ) \cos 4 θ \cos 7 θ \\ = \frac{1}{2 \times 4 \sin θ} (2 \sin 4 θ \cos 4 θ) \cos 7 θ \\ = \frac{1}{2 \times 8 \sin θ} [2 \sin 8 θ \cos 7 θ] \\ = \frac{1}{16 \sin θ} [\sin (15 θ) + \sin θ] \end{array}$
when $θ = \frac{π}{15}, f (θ) = \frac{1}{16}$

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