If sin θ1 + sin θ2 + sin θ3 = 3, then write the value of cos θ1 + cos θ2 + cos θ3.
Given that sin θ1 + sin θ2 + sin θ3 = 3
We know that in general the maximum value of sin θ = 1 when θ = π/2
As sin θ1 + sin θ2 + sin θ3 = 3
⇒ θ1= θ2 = θ3 = π/2.
The above case is the only possible condition for the given condition to satisfy.
∴ cos θ1 + cos θ2 + cos θ3
⇒ cos π/2 + cos π/2 + cos π/2
⇒ 0+0+0
⇒ 0.