જો 0

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. . .

Similar Questions

$6({\sin ^6}\theta + {\cos ^6}\theta ) - 9({\sin ^4}\theta + {\cos ^4}\theta ) + 4 = . . . $

જો $\sin x + {\sin ^2}x = 1$, તો ${\cos ^{12}}x + 3{\cos ^{10}}x + 3{\cos ^8}x + {\cos ^6}x - 2 =$

જો $x = \sec \,\phi - \tan \phi,y = {\rm{cosec}}\phi+ \cot \phi,$ તો

મૂલ્ય શોધો. $\cot \left(-\frac{15 \pi}{4}\right)$

આપેલ પૈકી ક્યૂ વિધાન અસત્ય છે.?