Question

Prove that sin(theta)+sin2(theta)/1+cos(theta)+cos2(theta)=tan(theta)?

Answer 1

See the proof below

Explanation:

Reminder :

`sin(2theta)=2sinthetacostheta`

`cos(2theta)=2cos^2theta-1`

`tantheta=sintheta/costheta`

Therefore,

`LHS=(sintheta+sin2theta)/(1+costheta+cos2theta)`

`=(sintheta+2sinthetacostheta)/(1+costheta+2cos^2theta-1)`

`=(sinthetacancel((1+2costheta)))/(costhetacancel((1+2costheta)))`

`=tantheta`

`=RHS`

`QED`