If sinx+cosx=0, then sinx=

sin x+cos x=0 cos x=-sin x 1-sin2x=sin x sin2x+sin x-1=0 sin x=-1±1+42 =5-12

If sinx+cosx=0, then sinx=

sin x+cos x=0 cos x=-sin x 1-sin2x=sin x sin2x+sin x-1=0 sin x=-1±1+42 =5-12

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If $\sqrt{sinx} + cosx = 0,$ then $sinx =$

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$\frac{\sqrt{5} + 1}{2}$

$\frac{\sqrt{5} - 1}{8}$

$\frac{\sqrt{5} - 1}{2}$

$\frac{\sqrt{5} + 1}{8}$

answer is D.

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Detailed Solution

$\sqrt{\sin x} + \cos x = 0 \cos x = - \sqrt{\sin x} 1 - \sin^{2} x = \sin x \sin^{2} x + \sin x - 1 = 0 \sin x = \frac{- 1 \pm \sqrt{1 + 4}}{2} = \frac{\sqrt{5} - 1}{2}$

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