Question

Prove
SinA (1+ tanA) + cosA (1+ cotA) = secA + cosecA
I want answer with STEPS....

Answer 1

LHS:

sinA(1+tanA) + cosA(1 + cotA)

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

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

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

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

We know that sin^2A + cos^2A = 1

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

cosecA + secA.


LHS = RHS.

Hope this helps!