Question

Value of theta satisfying sin7theta = sin4 theta - sin theta and theta belongs to (0, pi/2) are​

Answer 1

Answer:

Value of $\theta\:\:is\:\:\frac{\pi}{9}$

Step-by-step explanation:

Given: $sin\,7\theta=sin\,4\theta-sin\,\theta$

To find: Value of $\theta$ such that $\theta\epsilon(0,\frac{\pi}{2})$

Consider,

$sin\,7\theta=sin\,4\theta-sin\,\theta$

$sin\,7\theta+sin\,\theta=sin\,4\theta$

$2sin\,(\frac{7\theta+\theta}{2})cos\,(\frac{7\theta-\theta}{2})=sin\,4\theta$

$2sin\,4\theta\:\,cos\,3\theta=sin\,4\theta$

$2cos\,3\theta=1$

$cos\,3\theta=\frac{1}{2}$

$cos\,3\theta=cos\,\frac{\pi}{3}$

$\implies3\theta=\frac{\pi}{3}$

$\theta=\frac{\pi}{9}$

Therefore, Value of $\theta\:\:is\:\:\frac{\pi}{9}$

Answer 2

Answer:π/9

Step-by-step explanation: