`tan(2tan^(- 1)sqrt((1+costheta)/(1-costheta)))+tantheta=0`

Prove the following trigonometric identities: sqrt((1-sintheta)/(1+sintheta))=sectheta-tantheta sqrt((1+costheta)/(1-costheta))=cos e ctheta+cottheta

costheta(tantheta+2)(2tantheta+1)=?

Prove that sqrt((1+costheta)/(1-costheta))+sqrt((1-costheta)/(1+costheta))=2cosectheta

Prove the following: tan^-1(sqrt(frac{1-costheta}{1+costheta})) = frac{theta}{2} , if theta lies in (-pi,pi)

sintheta/(1-cottheta)+costheta/(1-tantheta)=

costheta=1/sqrt(2) and tantheta=-1

(i) ("sin"theta "tan"theta)/(1-costheta)=1sectheta (1+costheta)/(1-costheta)=("tan"^2theta)/((sectheta-1))^2

If 2tan^(-1)(costheta)=tan^(-1)(2cos e ctheta),(theta!=0) , then find the value of theta