Question

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

Answer 1

Let us consider the LHS: (cosec x – sin x) (sec x – cos x) (tan x + cot 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,

1 = RHS

∴ LHS = RHS

Thus proved.