How do you prove $\frac{1 - cos x}{sin x} = tan (\frac{x}{2})$ $(1- cosx)/sinx = tan(x/2)$ ?

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How do you prove $\frac{1 - cos x}{sin x} = tan (\frac{x}{2})$ $(1- cosx)/sinx = tan(x/2)$ ?

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Answer 1 · 2017-02-02T10:58:29

See the Proof given in the Explanation Section.

Explanation:

Recall that, $1 - cos θ = 2 {sin}^{2} (\frac{θ}{2}), and, sin θ = 2 sin (\frac{θ}{2}) cos (\frac{θ}{2})$ $1-cos theta=2sin^2 (theta/2), and, sin theta=2sin(theta/2)cos(theta/2)$ .

Using these, we have,

$"The L.H.S.="{cancel2sin^cancel2(x/2)}/(cancel(2sin(x/2))cos(x/2)}$

$=sin(x/2)/cos(x/2)$

$=tan(x/2)$

$="the R.H.S."$

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How do you prove $\frac{1 - cos x}{sin x} = tan (\frac{x}{2})$ $(1- cosx)/sinx = tan(x/2)$ ?

1 Answer

Explanation:

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How do you prove $\frac{1 - cos x}{sin x} = tan (\frac{x}{2})$ $(1- cosx)/sinx = tan(x/2)$ ?