AM-2494

Basic trigonometric identities

A Math · Secondary 4 · Medium · Basic trigonometric identities

Prove the identity

\dfrac{1-\cos x}{1+\cos x}=\tan^2\dfrac{x}{2}

. Which of the following is the correct first algebraic step?

$\tan^2\dfrac{x}{2}=\dfrac{\sin^2(x/2)}{\cos^2(x/2)}$
$\tan^2\dfrac{x}{2}=\dfrac{1-\cos x}{\sin x}$
$\tan^2\dfrac{x}{2}=\dfrac{\cos^2(x/2)}{\sin^2(x/2)}$
$\tan^2\dfrac{x}{2}=\dfrac{1+\cos x}{1-\cos x}$

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