Question

Solve the equations
$\sin (\theta -\varphi )=\frac{1}{2}$, and $\cos (\theta +\varphi )=\frac{1}{2}$.

Answer 1

$\sin (\theta -\varphi )=\frac{1}{2}=\sin {30}^{\circ }$

$⟹\theta -\varphi ={30}^{\circ }$.................(i)

$\cos (\theta +\varphi )=\frac{1}{2}=\cos {60}^{\circ }$

$⟹\theta +\varphi ={60}^{\circ }$.................(ii)

By solving (i) & (ii) we get,

$\theta ={45}^{\circ }$ and $\varphi ={15}^{\circ }$