Prove that `(1+costheta+sintheta)/(1-costheta+sintheta)=cot(theta/2)`

Prove that : (1+costheta- sin^(2)theta)/(sintheta+sinthetacostheta)=cottheta

Prove that sintheta/(1-costheta)=cosectheta+cot theta

prove that- (sintheta+1-costheta)/(costheta-1+sintheta)=(1+sintheta)/costheta

Prove that, 1/(costheta-cos3theta)+1/(costheta-cos5theta)+1/(costheta-cos7theta)+…+to n terms = 1/(2sintheta) [cottheta-cot(n+1)theta]

Prove that : (1+sintheta)/(costheta)+(costheta)/(1+sintheta)=2sectheta

Prove that : (sintheta-costheta)/(sintheta+costheta)+(sintheta+costheta)/(sintheta-costheta)=(2)/(2sin^(2)theta-1)

If cos theta-4sintheta=1, the sintheta+4costheta=

Evaluate : 1/costheta + sintheta/costheta = ?

Prove that : (1-costheta)/(sintheta)+(sintheta)/(1-costheta)=2"cosec "theta

Prove that : (sintheta)/(1+costheta)+(1+costheta)/(sintheta)=2"cosec"theta