Question

Tan\theta =2sin\theta

Answer 1

`\bf tan(\theta)=2sin(\theta)\qquad \begin{cases} tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad thus \end{cases}\\\\ -----------------------------\\\\ \cfrac{sin(\theta)}{cos(\theta)}=2sin(\theta)\implies \cfrac{sin(\theta)}{2sin(\theta)}=cos(\theta)\implies \cfrac{1}{2}=cos(\theta) \\\\\\ \textit{now, taking }cos^(-1)\textit{ to both sides} \\\\ cos^(-1)\left( \cfrac{1}{2} \right)=cos^(-1)[cos(\theta)]\implies cos^(-1)\left( \cfrac{1}{2} \right)=\measuredangle \theta`