Prove that `(cot theta -cos theta )/( cot theta +cos theta ) =(cos ec theta -1)/( cosec theta +1) `

(cot theta + "cosec" theta -1)/( cot theta - "cosec" theta +1) is

Prove that sqrt(cot^(2)theta-cos^(2)theta)=cottheta.costheta

Prove that (sin theta -cos theta+1 )/( sin theta + cos theta -1) =(1)/( sec theta -tan theta ) [use the identity sec ^(2) theta =1 +tan ^(2) theta ]

Prove that cot theta-tan theta=2cot 2 theta .

Show that (cosec theta -cot theta )^(2) =(1-cos theta )/( 1+cos theta )

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

Prove that cos (pi + theta) = - cos theta

Show that (1)/( cos theta ) -cos theta =tan theta .sin theta

Solve cot theta + tan theta=2 cosec theta .