Prove that 1 - cos2x + sinx/sin2x + cosx = tanx

Question

Prove that

\(\frac{1\,-\,cos2x\,+\,sinx}{sin2x\,+\,cosx}=tanx\)

1 - cos2x + sinx/sin2x + cosx = tanx

Answer 1

To prove: \(\frac{1\,-\,cos2x\,+\,sinx}{sin2x\,+\,cosx}=tanx\)

Taking LHS,

We know that,

1 – cos 2x = 2 sin²x & sin 2x = 2 sinx cosx

Taking sinx common from the numerator and cosx from the denominator

= \(\frac{sinx}{cosx}\)

= tanx  [∵ tanθ = \(\frac{sin\theta}{cos\theta}\)]

= RHS

∴ LHS = RHS

Hence Proved