`((1-sin theta)(1+cos theta))/((cos theta*sin theta))+1`

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

If (cos theta_(1))/(cos theta_(2))+(sin theta_(1))/(sin theta_(2))=(cos theta_(0))/(cos theta_(2))+(sin theta_(0))/(sin theta_(2))=1 , where theta_(1) and theta_(0) do not differ by can even multiple of pi , prove that (cos theta_(1)*cos theta_(0))/(cos^( 2)theta_(2))+(sin theta_(1)*sin theta_(0))/(sin^(2) theta_(2))=-1

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

Prove the orthogonal matrices of order two are of the form [(cos theta,-sin theta),(sin theta,cos theta)] or [(cos theta,sin theta),(sin theta,-cos theta)]

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

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

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

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

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

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