Question:
If sin θ1 + sin θ2 + sin θ3 = 3, then write the value of cos θ1 + cos θ2 + cos θ3.
Solution:
Sine function can take the maximum value of 1.
If, $\sin \theta_{1}+\sin \theta_{2}+\sin \theta_{3}=3$, then we have:
$\sin \theta_{1}=1$
$\Rightarrow \theta_{1}=\frac{\pi}{2}$
Similarly, $\theta_{2}=\theta_{3}=\frac{\pi}{2}$
$\Rightarrow \cos \theta_{1}=\cos \theta_{2}=\cos \theta_{3}=0$
$\Rightarrow \cos \theta_{1}+\cos \theta_{2}+\cos \theta_{3}=0$