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Question

$\cos x+\sin x=\frac{1}{2}$

$\Rightarrow(\cos x+\sin x)^{2}=\frac{1}{4}$

$\Rightarrow \cos ^{2} x+\sin ^{2} x+2 \cos x \sin x=\frac{1}{4}$

$\

Vedclass · Accepted Answer

$ - \frac{{4 + \sqrt 7 }}{3}$

Vedclass · Answer

$\cos x+\sin x=\frac{1}{2}$

$\Rightarrow(\cos x+\sin x)^{2}=\frac{1}{4}$

$\Rightarrow \cos ^{2} x+\sin ^{2} x+2 \cos x \sin x=\frac{1}{4}$

$\left[\because \cos ^{2} x+\sin ^{2} x=1 	ext { and } 2 \cos x \sin x=\sin 2 xight]$

$\Rightarrow 1+\sin 2 x=\frac{1}{4}$

$\Rightarrow \sin 2 x=-\frac{3}{4},$ so $x$ is obtuse and

$\frac{2 	an x}{1+	an ^{2} x}=-\frac{3}{4}$

$\Rightarrow 3 	an ^{2} x+8 	an x+3=0$

$	an x=\frac{-8+\sqrt{64-36}}{6}$

$=\frac{-4+\sqrt{7}}{3}$

as $	an x<0$

$	an x=\frac{-4-\sqrt{7}}{3}$

જો $0 < x < \pi $ અને $\cos x + \sin x = \frac{1}{2}$ તો $\tan x$ મેળાવે. . .

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