Question

If $2\sin x+5\cos y+7\sin z=14$ then $7\tan$ $\frac{x}{2}+4\cos y-6\cos z=$

• A. $4$
• B. $-3$
• C. $11$
• D. $5$

Answer 1

The correct option is C $11$

As for real values of $x,y,z,\sin$ or $\cos$ value lies only in $[-1,1]$,

the given equation is possible if and only if each of $\sin \left(x\right),\cos \left(y\right),\sin \left(z\right)=1$

$\Rightarrow 2+5+7=14$

So $x=\frac{\pi }{2};\sin \frac{\pi }{2}=1$

$y=0;\cos \left(0\right)=1$

$z=\frac{\pi }{2};\sin \frac{\pi }{2}=1$

ii) Thus $\tan \frac{\pi }{2}=\tan \frac{\pi }{4}=1$

$\cos \left(z\right)=\cos \frac{\pi }{2}=0$

Hence $7\tan \frac{x}{2}+4\cos \left(y\right)-6\cos \left(z\right)=7+4-0=11$