Question

show that sqrt1+sinA/1-sinA=secA+tanA

Answer 1

Answer: √1+sina-/1-sina

multiplying numerator and denominator by √1+sina

(√1+sina)(√1+sina)/√(1-sina)(1+sina)

(√1+sina)²/√1-sin²a

1+sina/cosa

1/cosa + sina/cosa

seca + tana

HENCE PROVED

DON'T FORGET TO FOLLOW ME

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given:$\sqrt{\frac{1+sinA}{1-sinA}}$

To prove:$\sqrt{\frac{1+sinA}{1-sinA}}×\sqrt{\frac{1+sinA}{1+sinA}}$

then,

$→\sqrt{\frac{1+sinA}{1-sinA}×\frac{1+sinA}{1+sinA}}$

$→\sqrt{\frac{(1+sinA)²}{1-sinA×1+sinA}}$

$→\frac{\sqrt{1+sinA}}{\sqrt{1-sinA}}$

$→\frac{1+sinA}{\sqrt{cos²A-1}}$

$→\frac{1+sinA}{cosA}$

$→\frac{1}{cosA}+\frac{sinA}{cosA}$

$→\boxed{secA+tanA}$

$R.H.S$

Hence proved......