Prove the following trigonometrical identities
`sqrt((1+Costheta)/(1-costheta)) = |cosectheta + cot theta|`

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

Prove that sintheta/(1-costheta)=cosectheta+cottheta .

Prove the following identity : sqrt ((1-cos theta)/(1+cos theta)) = cosec theta-cot theta .

Prove the following identity : sqrt ((1+cos theta)/ (1-cos theta)) = cosec theta+cot theta

Solve the following trigonometric equation : sqrt3 cos theta -sin theta=1 .

Prove that (1-costheta)/(1+costheta)=(cosectheta-cottheta)^2 .

Solve the following trigonometric equation : sqrt2 sec theta -tan theta=1 .

Solve the following trigonometric equation : cosec theta= cot theta+sqrt3 .

Prove the following identity : (sin theta)/(1+cos theta)+ (tan theta)/(1+cos theta)= sec theta cosec theta- cot theta .

Solve the following trigonometric equation : 2 tan theta-cot theta-1=0 .