Learn how to solve differential calculus problems step by step online. Prove the trigonometric identity tan(x)-tan(x)sec(x)^2=-tan(x)^3. Starting from the left-hand side (LHS) of the identity. Factor the polynomial \tan\left(x\right)-\tan\left(x\right)\sec\left(x\right)^2 by it's greatest common factor (GCF): \tan\left(x\right). Apply the trigonometric identity: -\sec\left(\theta \right)^2+1=-\tan\left(\theta \right)^2. When multiplying exponents with same base you can add the exponents: -\tan\left(x\right)\tan\left(x\right)^2.

Prove the trigonometric identity tan(x)-tan(x)sec(x)^2=-tan(x)^3