Question

Prove the identity: cosec x(sec x – 1) – cot x(1 – cos x) = tan x – sin x

Answer 1

Let us consider the LHS: cosec x(sec x – 1) – cot x(1 – cos x)

On using the formulas

cosec θ = 1/sin θ;

sec θ = 1/cos θ;

tan θ = sin θ/cos θ;

cot θ = cos θ/sin θ

Then,

On using the formula, 1 – cos²x = sin²x;

tan x - sin x

= RHS

∴ LHS = RHS

Thus proved.