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

See explanation

Explanation:

We have to prove the identity

`tan((\Theta )/(2))=(sin\Theta)/(1+cos\Theta )`

We will take right hand side of the identity

`(sin\Theta)/(1+cos\Theta)=(2sin((\Theta )/(2))cos((\Theta )/(2)))/(1+[2cos^(2)((\Theta )/(2))-1])`

`=(2sin((\Theta )/(2))cos((\Theta )/(2)))/(2cos^(2)((\Theta )/(2)))=(sin((\Theta )/(2)))/(cos((\Theta )/(2)))`

`=tan((\Theta )/(2))` [ Tan θ will be positive since θ lies in 1st quadrant ]