Question

If 2 sin² θ - cos² θ = 2, then find the value of θ.​

Answer 1

Given : 2 sin² θ - cos² θ = 2

➺ 2 sin² θ - (1 - sin² θ) = 2

➺ 3 sin² θ - 1 = 2

➺ 3 sin² θ = 3

➺ sin² θ = 1

➺ sin θ = 1

➺ θ = 90°.

☆ Therefore,

• Hence, the value of θ is 90°.

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Answer 2

Given :

• 2sin²θ - cos²θ = 2

To Find :

• Value of θ = ?

Solution :

2sin²θ - cos²θ = 2

We know that cos²θ = 1 - sin²θ :

=> 2sin²θ - (1 - sin²θ) = 2

=> 2sin²θ - 1 + sin²θ = 2

=> 3sin²θ - 1 = 2

=> 3sin²θ = 2 + 1

=> 3sin²θ = 3

=> sin²θ = 3/3

=> sin²θ = 1

=> sinθ = √1

=> sinθ = 1

Now, we know that sin90° = 1 :

=> sinθ = sin90°

=> θ = 90°

Hence, value of θ is 90°.