Question

Please solve the question of trigonometry which I have attached with this question.
I'll be grateful to you.

Answer 1

I hope this answer helps.

Answer 2

Given:

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

On cross-multiplication, we get

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

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

We know that (a+b)^2 = a^2 + b^2 + 2ab

$\frac{2cosA + sinA}{cos^2A + sin^2A + 2sinAcosA - 1}$

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

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

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

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

secA + cosecA.


LHS = RHS


Hope this helps!