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, $\sin {\theta }_1+\sin {\theta }_2+\sin {\theta }_3=3$, then we have:

sin${\theta }_1$ = 1

⇒ ${\theta }_1$=$\frac{\mathrm{\pi }}{2}$
Similarly, ${\theta }_2={\theta }_3=\frac{\mathrm{\pi }}{2}$

$$\begin{gathered} \Rightarrow \cos {\theta }_1=\cos {\theta }_2=\cos {\theta }_3=0 \\ \Rightarrow \cos {\theta }_1+\cos {\theta }_2+\cos {\theta }_3=0 \end{gathered}$$