Question

If $\sin {\theta }_1+\sin {\theta }_2+\sin {\theta }_3=3,$ then $\cos {\theta }_1+\cos {\theta }_2+\cos {\theta }_3$is equal to

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

Answer: (D)

$0$

given $\sin {\theta }_1+\sin {\theta }_2+\sin {\theta }_3=3$
we know maximum value of $\sin \theta =1$ at $\theta =\frac{\pi }{2}$
so above equation only satisfy if $\sin {\theta }_1=1,\sin {\theta }_2=1,$and $\sin {\theta }_3=1$ and ${\theta }_1={\theta }_2={\theta }_3=\frac{\pi }{2}$
$\because \cos \frac{pi}{2}=0$
$\Rightarrow \cos {\theta }_1=0,\cos {\theta }_2=0,$and $\cos {\theta }_3=0$
So, $\cos {\theta }_1+\cos {\theta }_2+\cos {\theta }_3=0$
Hence, option ${}^{\prime }{D}^{\prime }$ is correct.