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Prove that : sqrt((1-sin theta)/(1+sin t...

Prove that : `sqrt((1-sin theta)/(1+sin theta))= {(sec theta- tan theta, if -pi/2 < theta< pi/2), (-sec theta+ tan theta, if pi/2 < theta< (3 pi)/2):}`.

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Prove the following identity : sqrt ((1+sin theta)/ (1-sin theta)) = {{:(sec theta+tan theta, if -pi/2 lt theta lt pi/2),( -sec theta-tan theta, if pi/2 lt theta lt (3pi)/2):} .

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Prove that (1+sin2theta)/(1-sin2theta)=((1+tantheta)/(1-tan theta))^(2)

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

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

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 : cos theta- sin theta= sqrt2 cos (theta+ pi/4) .

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

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

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
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