Question

prove tan(theta/2)=sin theta/1+cos theta for theta in quadrant 1 by filling in the calculations and reasons. PLEASE HELP!!!!

Answer 1

Answer:

See explanation

Step-by-step explanation:

We have to prove the identity

$tan(\frac{\Theta }{2})=\frac{sin\Theta}{1+cos\Theta }$

We will take right hand side of the identity

$\frac{sin\Theta}{1+cos\Theta}=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{1+[2cos^{2}(\frac{\Theta }{2})-1]}$

$=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{2cos^{2}(\frac{\Theta }{2})}=\frac{sin(\frac{\Theta }{2})}{cos(\frac{\Theta }{2})}$

$=tan(\frac{\Theta }{2})$ [ Tan θ will be positive since θ lies in 1st quadrant ]