Question

if sin theta 1 + sin theta 2 + sin theta is equal to 3 then find the value of cos theta + cos theta 2 + cos theta 3

Answer 1

cosθ1+cosθ2+cosθ3=0

Explanation:

Value of sine ratio ranges from −1 to 1 i.e. [−1,1]

Now as sinθ1+sinθ2+sinθ3=3

We must have each of them as 1

and hence θ1=θ2=θ3=90∘

and as cos90∘=0

cosθ1+cosθ2+cosθ3=0

Answer 2

The value of cos θ₁ + cos θ₂ + cos θ₃ = 0

Correct question : If sin θ₁ + sin θ₂ + sin θ₃ = 3 then find the value of cos θ₁ + cos θ₂ + cos θ₃

Given :

sin θ₁ + sin θ₂ + sin θ₃ = 3

To find :

The value of cos θ₁ + cos θ₂ + cos θ₃

Solution :

Step 1 of 3 :

Write down the given equation

Here the given equation is

sin θ₁ + sin θ₂ + sin θ₃ = 3

Step 2 of 3 :

Find the value of θ₁ , θ₂ , θ₃

sin θ₁ + sin θ₂ + sin θ₃ = 3

We know that the maximum value of sine of an angle is 1

∴ sin θ₁ + sin θ₂ + sin θ₃ = 3 gives

sin θ₁ = sin θ₂ = sin θ₃ = 1

∴ θ₁ = θ₂ = θ₃ = 90°

Step 3 of 3 :

Calculate the value of cos θ₁ + cos θ₂ + cos θ₃

θ₁ = θ₂ = θ₃ = 90°

∴ cos θ₁ + cos θ₂ + cos θ₃

= cos 90° + cos 90° + cos 90°

= 0 + 0 + 0

= 0

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