Question

If sin θ₁ + sin θ₂ + sin θ₃ = 3, then write the value of cos θ₁ + cos θ₂ + cos θ₃.

 

Answer 1

Sine function can take the maximum value of 1.
If, \[\sin \theta_1 + \sin \theta_2 + \sin \theta_3 = 3\]
 sin \[\theta_1\] = 1
⇒ \[\theta_1\] = \[\frac{\pi}{2}\]
Similarly,

\[\theta_2 = \theta_3 = \frac{\pi}{2}\]

\[\Rightarrow \cos \theta_1 = \cos \theta_2 = \cos \theta_3 = 0\]
\[ \Rightarrow \cos \theta_1 + \cos \theta_2 + \cos \theta_3 = 0\]