Question

Solve:Sin3theta(2cos2theta-1)=0​

Answer 1

Step-by-step explanation:

We have,

$\sin(3 \theta ) (2 \cos(2\theta) - 1) = 0$

$\implies \sin( 3\theta) = 0 \: \: or \: \: 2 \cos(2\theta) - 1 = 0$

$\implies3\theta = n\pi \: \: or \: \: \cos(2\theta) = \frac{1}{2}$

$\implies\theta = \frac{n\pi}{3} \: \: or \: \: 2\theta = 2m\pi + \frac{\pi}{3} \: \: or \: \: 2\theta = 2m\pi - \frac{\pi}{3}$

$\implies\theta = \frac{n\pi}{ 3} \: \: or \: \: \theta = m\pi + \frac{\pi}{6} \: \: or \: \: \theta = m\pi - \frac{\pi}{6} \\ for \: \: all \: \: m \: \: and \: \: n \: \: \in \: \: integers$