First slide

Multiple and sub- multiple Angles

Question

If $0 < x < π$ and $\cos x + \sin x = \frac{1}{2},$ then $\tan x =$

Moderate

A

$\frac{(4 - \sqrt{7})}{3}$
B

$- \frac{(4 + \sqrt{7})}{3}$
C

$\frac{(1 + \sqrt{7})}{4}$
D

$\frac{(1 - \sqrt{7})}{4}$

Solution

Put $\cos x = \frac{1 - \tan^{2} \frac{x}{2}}{1 + \tan^{2} \frac{x}{2}}, \sin x = \frac{2 \tan \frac{x}{2}}{1 + \tan^{2} \frac{x}{2}}$

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