Question

If $\sin x=\cos y,\sqrt{6}\sin y=\tan z$ and $2\sin z=\sqrt{3}\cos x$; $u,v,w$ denotes respectively ${\sin }^{2}x,{\sin }^{2}y,{\sin }^{2}z$ then the value of the triplet $(u,v,w)$ is

• A. $(1,0,0)$
• B. $(0,1,0)$
• C. $(1/2,1/2,3/4)$
• D. $(1/2,3/4,1/2)$

Answer 1

The correct option is A $(1,0,0)$

Let $x=\frac{\pi }{2}\Rightarrow sinx=1cosy=sinx=1\Rightarrow y=0\Rightarrow siny=02sinz=\sqrt{3}cosx=\sqrt{3}.0=0\Rightarrow sinz=0u={sin}^{2}x=1,v={sin}^{2}y=0,z={sin}^{2}z=0$