Question

√1+sin A / √1- sin A= sec A + tan A

Answer 1

Hey friend ☺

Here is your answer

TO PROVE :

√(1+sinA)/√(1-sinA)=secA +tanA

PROOF :

LHS :

=√(1+sinA)/√(1-sinA)

RATIONALISING DENOMINATOR

=[√(1+sinA)×√(1+sinA)]÷[√(1-sinA)×√(1+sinA)]

=[√(1+sinA)²] / [√(1-sin²A) ]

[USING cos²A+sin²A=1]

=[√(1+sinA)²] / [√cos²A]

=(1+sinA)/cosA

=(1/cosA)+(sinA/cosA)

=secA+tanA

=RHS

HOPE THIS HELPS YOU