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  4. If 1 + cos x = k, where x is acute, then sin(x/2) is

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Q. If $1 + cos \,x = k$, where $x$ is acute, then $sin(x/2)$ is

Trigonometric Functions

Solution:

$1+cos\,x=k$
$\Rightarrow 2\,cos^{2} \frac{x}{2}=k$
$\Rightarrow 1-sin^{2} \frac{x}{2}=\frac{k}{2}$
$\Rightarrow sin \frac{x}{2}=\sqrt{\frac{2-k}{2}}$