Prove that :
`tan theta - cot theta = (2 sin^(2) theta - 1)/(sin theta cos theta)`

Prove the following trigonometric identities: tan theta-cot theta=(2sin^(2)theta-1)/(sin theta cos theta)

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

Prove that (cos^(2) theta)/(1-tan theta)+(sin^(3) theta)/(sin theta - cos theta) =1 + sin theta cos theta .

Prove the following trigonometric identities: cot theta-tan theta=(2cos^(2)theta-1)/(sin theta cos theta)

Prove that : (1+ sin theta - cos theta) / (1+ sin theta + cos theta ) = tan (theta/2)

Prove that : (1+ sin theta - cos theta) / (1+ sin theta + cos theta ) = tan (theta/2)

Prove that (1+ cot theta + tan theta ) ( sin theta - cos theta) = (sec theta )/(cosec^(2) theta) - (cosec theta)/(sec^(2)theta) .

prove that sin theta + tan theta = (cos theta) / (1-sin theta)

Prove that: (sin theta - cos theta +1)/(sin theta + cos theta -1) = (1)/(sec theta - tan theta)

Prove that : ( sin theta- cos theta +1)/( sin theta +cos theta -1) = (1)/( sec theta - tan theta)