`d/(d theta)(tan^(- 1)((1-costheta)/(sintheta)))` equals, if `-pi lt theta lt pi`

If f(theta) = sin(tan^(-1)(sintheta/sqrt(cos2theta))) , where -pi/4 lt theta lt pi/4, then the value of d/(d(tantheta))\ f(theta) is

If f(theta) = sin(tan^(-1)(sintheta/sqrt(cos2theta))) , where -pi/4 lt theta lt pi/4, then the value of d/(d(tantheta))\ f(theta) is

Solve sintheta+sqrt(3)costheta geq 1 , -pi lt theta lt pi

If f(theta) = sin(tan^(-1)(("sin theta)/(sqrt(cos 2 theta)))) , where -pi/4 lt theta lt pi/4 , then the value of d/(d(tan theta)) f(theta) is

costheta - sintheta = 1/sqrt(2) (-pi lt theta lt pi)

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):} .

Solve tan theta tan 4theta=1 for - lt theta lt pi .

Solve tan theta tan 4theta=1 for - lt theta lt pi .