How do you express sin x/2 in terms of cos x using the double angle identity?

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How do you express sin x/2 in terms of cos x using the double angle identity?

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Answer 1 · 2015-10-18T05:13:51

Express sin (x/2) in terms of cos x.

Ans: $sin (\frac{x}{2}) = \sqrt{\frac{1 - cos x}{2}}$ $sin (x /2) = sqrt((1 - cos x)/2)$

Explanation:

By applying the trig identity: $cos 2 a = 1 - 2 {sin}^{2} a$ $cos 2a = 1 - 2sin^2 a$ , we get:
$cos x = 1 - 2 {sin}^{2} (\frac{x}{2})$ $cos x = 1 - 2sin^2 (x/2)$
$2 {sin}^{2} (\frac{x}{2}) = 1 - cos x$ $2sin^2 (x/2) = 1 - cos x$
${sin}^{2} (\frac{x}{2}) = \frac{1 - cos x}{2}$ $sin^2 (x/2) = (1 - cos x)/2$
$sin (\frac{x}{2}) = \pm \sqrt{\frac{1 - cos x}{2}}$ $sin (x/2) = +- sqrt((1 - cos x)/2)$

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How do you express sin x/2 in terms of cos x using the double angle identity?

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