If `tan(theta/2)=(cosectheta-sin theta)` then `tan^2 (theta/2)=`

If tan (theta)/(2) =cosec theta - sin theta then tan^(2)(theta/2)=

tan theta . sin^2 theta = ?

Show that : (1+ tan theta/2)/(1-tan theta/2) = (1+sin theta)/(cos theta) = tan (pi/4 + theta/2)

Cosider the following : 1. tan ^(2) theta - sin ^(2) theta = tan ^(2) theta sin ^(2) theta 2. (cosec theta - sin theta ) (sec theta - cos theta ) (tan theta + cot theta ) =1 Which of the above is/are correct ?

If cos^2theta-sin^2 theta = 1/2 . Then tan theta =

Prove that tan^2 (theta)-sin^2 (theta)= tan^2 (theta) sin^2 (theta)

(1+2sin theta+sin^(2)theta)/(cos^(2)theta)=(sec theta+tan theta)/(sec theta-tan theta)

(2sin theta-sin2 theta)/(2sin theta+sin2 theta)=tan^(2)((theta)/(2))

Prove that : (sec theta-tan theta)/(sec theta+tan theta)= 1-2 sec theta tan theta+ 2 tan^2 theta .

tan^2theta-sin^2theta=tan^2theta.sin^2theta