Question

Prove that cosA/1+sinA + 1+sinA/cosA = 2secA

Answer 1

LHS:

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

On cross multiplication, we get

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

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

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

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

$\frac{2}{cosA}$

$2 secA.$


LHS = RHS.


Hope this helps!