Question

If $\sin {\theta }_1+\sin {\theta }_2+\sin {\theta }_3+\sin {\theta }_4=4$, then what is the value of $\cos {\theta }_1+\cos {\theta }_2+\cos {\theta }_3+\cos {\theta }_4$?

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is A $0$

$\sin {\theta }_1+\sin {\theta }_2+\sin {\theta }_3+\sin {\theta }_4=4$

$\sin \theta \le 1$ $\forall \theta$
So, the value of the given function is its maximum value which can only be obtained, when $\sin \theta =1$

$⟹\sin {\theta }_1=\sin {\theta }_2=\sin {\theta }_3=\sin {\theta }_4=\mathrm{1........}when{\theta }_1={\theta }_2={\theta }_3={\theta }_4=\frac{\pi }{2}$

$⟹\cos {\theta }_1=\cos {\theta }_2=\cos {\theta }_3=\cos {\theta }_4=0$

$\therefore \cos {\theta }_1+\cos {\theta }_2+\cos {\theta }_3+\cos {\theta }_4=0$

So, the answer is option (A)