√1+sinA/√1-sinA = tanA + secA
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To prove :- ✓1+sinA/✓1-sinA = tanA + secA
Rationalize:-
= ✓ 1+ sinA/ ✓ 1-sinA × ✓1+sinA / 1+sinA
= (✓1+sinA)^2/ (✓1^2 - sin^2A)
= 1+ sinA/ ✓1-(1-cos^2A) ( Sin^2A+ Cos^A = 1)
= 1+ sinA/ ✓cos^2A. ( Sin^2A = 1- Cos^2A)
= 1+ sinA/ cosA
= 1/cosA + sinA/cosA
= secA + tanA
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