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

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

(1+sin 2theta+cos 2theta)/(1+sin2 theta-cos 2 theta) =

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

Prove that cos^6 theta+ sin^6 theta= 1-3sin^2 theta cos^2 theta

Prove that : (sin 5theta + sin 3theta)/(cos 5theta + cos 3theta) = tan 4theta

Prove that : (sin theta + sin 3theta + sin 5theta)/(cos theta + cos 3theta + cos 5theta) = tan 3theta

Prove that : (sin theta + sec theta) ^(2) + (cos theta + cosec theta) ^(2) = (1 + sec theta cosec theta) ^(2).

Prove that : (sin 5theta - 2 sin 3theta + sin theta)/(cos 5theta -cos theta) = tan theta

(1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=?

Prove that : sin theta cos^3 theta - cos theta sin^3 theta = 1/4 sin4theta .