Question

Given that $\sin \theta =\frac{1}{2}$ and $\sin \varphi =\frac{1}{3}$, If the value of $\cos (\theta -\varphi )$ $-\cos (\theta +\varphi )$ is $\frac{1}{m}$. Find the value of $m$.

Answer 1

$\to \cos (\theta -\varphi )-\cos (\theta +\varphi )=2\sin \theta \sin \varphi$

$\Rightarrow 2\sin \theta \sin \varphi =2\times \frac{1}{2}\times \frac{1}{3}=\frac{1}{3}=\frac{1}{m}$

$\to m=3$