If sin θ1 + sin θ2 + sin θ3 + sin θ4 = 4, then what is the value of cos θ1 + cos θ2 + cos θ3 + cos θ4?

If sin θ1 + sin θ2 + sin θ3 + sin θ4 = 4, then what is the value of cos θ1 + cos θ2 + cos θ3 + cos θ4? Correct Answer 0

Concept:

• -1 ≤ sin θ ≤ 1
• 1 ≤ cos θ ≤ 1

Calculation:

Given: sin θ₁ + sin θ₂ + sin θ₃ + sin θ₄ = 4

As we know that maximum value of sin θ is 1,

⇒ sin θ₁ + sin θ₂ + sin θ₃ + sin θ₄ = 1 + 1 + 1 + 1

So, the value of the given function is its maximum value which can only be obtained, when sin θ = 1

∴ θ₁ = θ₂ = θ₃ = θ₄ = π/2

Now,

⇒ cos θ₁ + cos θ₂ + cos θ₃ + cos θ₄

= cos (π/2) + cos (π/2) + cos (π/2) + cos (π/2)

= 0