Question

Prove that sinθ-cosθ+1/sinθ+cosθ- 1 = 1/secθ- tanθ using the identity sec²θ = 1 + tan²θ

Answer 1

Since we will apply the identity involving secθ and tanθ, let us first convert the LHS (of the identity we need to prove) in terms of secθ and tanθ by dividing numerator and denominator by cosθ

which is the RHS of the identity, we are required to prove.