Prove the following trigonometrical identities
`sec theta (1-sintheta)(Sectheta+tantheta) = 1`

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

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

Solve the following trigonometric equation : sec theta- tan theta= sqrt3 .

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

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

Prove the following identity : (1-sin theta)/(1+sin theta)= (sec theta-tan theta)^2 .

Solve the following trigonometric equation : tan theta+ sec theta= sqrt3 .

Prove the following identity : sqrt ((1+sin theta)/ (1-sin theta)) = {{:(sec theta+tan theta, if -pi/2 lt theta lt pi/2),( -sec theta-tan theta, if pi/2 lt theta lt (3pi)/2):} .

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

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