MHB Proving Trig Identity: (Sin2x-tanx)/cos2x=tanx

[paix1988]

May someone kindly assist me to prove this trig identity

(Sin2x-tanx) / cos2x = tanx

Thank you for your assistance

 

[Siron]

May someone kindly assist me to prove this trig identity

(Sin2x-tanx) / cos2x = tanx

Thank you for your assistance

Making use of the identities $\sin 2x = 2 \sin x \cos x$ and $\tan x = \sin x / \cos x$ we can write the RHS as:
$$\frac{2 \sin x \cos x -\frac{\sin x}{\cos x}}{\cos 2x}.$$
To proceed, write the numerator as one fraction (thus with denominator $\cos x$) and factorize!