`cosec theta sqrt(1-cos^(2)theta)=1`

Prove that sqrt((1+costheta)/(1-costheta))+sqrt((1-cos theta)/(1+cos theta))=2 " cosec"theta.

Consider the following: 1. sqrt((1-cos theta)/(1+cos theta)) = "cosec" theta -cot theta 2. sqrt((1+cos theta)/(1-cos theta))="cosec" theta +cot theta Which of the above is/are identity/ identities?

Prove each of the following identities : (i) (1+ cos theta)(1- cos theta)(1+ cot^(2) theta)=1 (ii) "cosec" theta (1+ cos theta)("cosec" theta - cot theta)=1

Prove each of the following identities : (i) sqrt((1+ sin theta)/(1- sin theta)) = ( sec theta + tan theta) (ii) sqrt((1- cos theta)/(1+ cos theta))= ("cosec" theta - cot theta) (iii) sqrt((1+ cos theta)/(1- cos theta))+ sqrt((1- cos theta)/(1+ cos theta)) = 2 "cosec" theta

Prove that sqrt ((1-cos theta )/( 1+cos theta ) ) = cosec theta -cot theta , 0le theta le 90 ^(@)

sqrt(cosec^2theta-sin^2theta-cos^2theta) = …………….

Prove the following trigonometric identities: sqrt((1-sin theta)/(1+sin theta))=sec theta-tan thetasqrt((1+cos theta)/(1-cos theta))=csc theta+cot theta

If (1/(1+cosec theta ) - 1/(1-cosec theta ))cos theta= 2 , 0^circ lt theta lt 90^circ , then the value of sin^(2) theta + cot^(2) theta + sec^(2) theta is: यदि (1/(1+cosec theta ) - 1/(1-cosec theta ))cos theta= 2 , 0^circ lt theta lt 90^circ , है,तो sin^(2) theta + cot^(2) theta + sec^(2) theta का मान हैः

Prove that (1+ cot theta + tan theta ) ( sin theta - cos theta) = (sec theta )/(cosec^(2) theta) - (cosec theta)/(sec^(2)theta) .