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Prove that sec theta+tan theta=root (1+sin theta/1-sin theta)

Prove that sec theta+tan theta=root (1+sin theta/1-sin theta)

Grade:10

1 Answers

Soumendu Majumdar
159 Points
3 years ago
Dear Student,
First to make the problem easier square both sides L.H.S & R.H.S
so we need to prove (sec A – tan A)^2 = ( 1 + sin A)/( 1 – sin A)
Now L.H.S= { (1 – sin A)/(cos A)}^2
                 = { (1- sin A)^2}/(1- sin^2 A) = {(1- sin A)^2}/(1 + sin A)(1- sin A)
                 = ( 1 – sin A)/(1 + sin A) = R.H.S   [Proved]
Hope it helps!

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