Question

1+sina/cosa+cosa/1+sina=2seca

Answer 1

Hi !

$\frac{1+ sinA}{cosA} + \frac{cosA}{1+ sinA}$

Cross multiplication,

$\frac{(1+sinA) ^{2} + cos ^{2}A }{(1+sinA)cosA}$

$\frac{1 + 2sinA + sin ^{2}A + cos ^{2}A }{(1+sinA)cosA}$

we know that ,

sin²A + cos²A = 1

$\frac{1 + 1 + 2 sinA}{(1+sinA)cosA}$

$\frac{2 + 2sinA}{(1+sinA)(cosA)}$

$\frac{2(1+sinA)}{(1+sinA)(cosA)}$

1 + sinA gets cancelled ,


$\frac{2}{cosA}$

2* 1/cosA

We know that , 1/cosA = secA

hence,

2*secA = 2secA = RHS 

proved !