#### Question

Prove the following.

tan^{4}θ + tan^{2}θ = sec^{4}θ - sec^{2}θ

#### Solution

Taking LHS

tan^{4}θ + tan^{2}θ

= tan^{2}θ( tan^{2}θ + 1)

= (sec^{2}θ - 1)(sec^{2}θ) [1 + tan^{2}θ = sec^{2}θ]

= sec^{4}θ - sec^{2}θ

= RHS

Is there an error in this question or solution?

Solution Prove the Following. Tan4θ + Tan2θ = Sec4θ - Sec2θ Concept: Trigonometric Ratios of Complementary Angles.