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Prove that (sin theta- "cosec" theta ...

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

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

Prove that : sin 2 theta= 2sin theta cos theta .

(cosec theta -sin theta ) (sec theta - cos theta ) (tan theta + cot theta ) = 1.

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

Prove the following identity : (sec theta-cos theta) (cosec theta-sin theta)=1/(tan theta+ cot theta) .

Prove the following identity : (sin theta+ sec theta)^2 +(cos theta+ cosec theta)^2= (1+ sec theta cosec theta)^2 .

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

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

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

Prove the following identity : (cot theta+ cosec theta -1)/(cot theta- cosec theta +1)= (1+ cos theta)/(sin theta) .