Question

prove that sin 2A (1+cot2A)=1

Answer 1

$identity : \: {cosec}^{2} a - cot^{2} a = 1$

LHS:—

$= > (1 + cot^{2} a)sin^{2} \: a$

$= > cosec^{2} a \times sin^{2} \: a$

$= > \frac{1}{sin^{2} \: a} \times sin^{2} a$

$= > 1$

RHS:—

$= > 1$

Therefore, LHS = RHS.

HENCE, PROVED.