If sin θ 1 + sin θ 2 + sin θ 3 = 3, then write the value of cos θ 1 + cos θ 2 + cos θ 3 .

Question

Philoid · Accepted Answer

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.

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