Question

prove that cosa/1-sina+cosa/1+sina=2seca

Answer 1

Given Equation is $\frac{cos theta}{1 - sin theta} + \frac{costheta}{1 + sin theta}$

On cross-multiplication, we get

$\frac{cos theta(1 + sin theta) + cos theta(1 - sin theta)}{(1 - sin theta)(1 + sin theta)}$

$\frac{costheta + cos theta * sin theta + cos theta - cos theta * sin theta}{1 - sin^2 theta}$

$\frac{2 cos theta}{cos^2 theta}$

$\frac{2}{cos theta}$

$2( \frac{1}{cos theta} )$

We know that 1/cos theta = sec theta

2 sec theta.


Hope this helps!