Question

Prove the following Identity: sec^2x-1/cotx = tan^3x


Help would be very welcomed thank you.

Answer 1

Begin with the LHS:\[\frac{\sec^2x - 1}{\cot x} \] Substitute \(\sec^2x - 1 = \tan^2x\) \[\frac{\tan^2x}{\cot x}\]

Write \(\frac{\tan^2x}{\cot x}\) as \[\tan^2x \div \cot x\]Which becomes
\[\tan^2x \times \tan x\]