Question

Prove the trigonometric identity
(tan x + cot x)/(csc x * cos x) = sec^2 x​

Answer 1

To prove the trigonometric identity (tan x + cot x)/(csc x * cos x) = sec^2 x, we can simplify the expression step by step:

(tan x + cot x)/(csc x * cos x)

= (sin x / cos x + cos x / sin x) / (1 / sin x * cos x)

= [(sin^2 x + cos^2 x) / (sin x * cos x)] / (1 / sin x * cos x)

= [(sin^2 x + cos^2 x) / (sin x * cos x)] * (sin x * cos x / 1)

= sin^2 x + cos^2 x

= 1

= sec^2 x

Hence, we have shown that the left-hand side (LHS) is equal to the right-hand side (RHS), proving the trigonometric identity.