Question

Solve $\theta$:
$\sin \theta +2cos\theta =1,cos\theta -2sin\theta =2$

Answer 1

$\sin \theta +2\cos \theta =1$ ……….$\left(1\right)$

$\cos \theta -2\sin \theta =2$ ……….$\left(2\right)$

$2\sin \theta +4\cos \theta =2$ ………..$\left(3\right)$

$\left(2\right)+\left(3\right)$

$\Rightarrow 5\cos \theta =4$

$\cos \theta =\frac{4}{5}$

$\theta ={\cos }^{-1}\left(\frac{4}{5}\right)$.