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Prove that (cosec theta - sectheta) (Cot...

Prove that `(cosec theta - sectheta) (Cottheta - tantheta) = (cosectheta + sectheta)(Sectheta cosectheta-2)`

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Prove that (cosectheta+cottheta)/(cosectheta-cottheta) =((1+costheta)/sintheta)^2 .

Prove that (cosectheta+cottheta)(1-costheta)=sintheta .

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

Prove that (1-sintheta)/(1+sintheta)=(sectheta-tantheta)^2 .

Prove that sintheta(cosectheta-sintheta)=cos^2theta .

Prove that (1 +cot theta -cosec theta )(1+tan theta +sec theta )=2.

Prove that (1-costheta)/(1+costheta)=(cosectheta-cottheta)^2 .

Prove that cottheta+tantheta=secthetacosectheta .

Prove that sqrt((sectheta-tantheta)/(sectheta+tantheta))=sectheta-tantheta .