1.

Solve for θ, cos²θ / (cot²θ – cos² θ) = 3

Answer»

GIVEN:

cos²θ / (cot²θ – cos² θ) = 3

To find:

The value of the θ.

Solution:

Let's take the LHS of the given EQUATION;

  • cos²θ / (cot²θ – cos² θ)
  • cos²θ / (cos²θ/sin²θ – cos² θ)
  • cos²θ /cos²θ (1/sin²θ – 1)
  • 1 /1 (1/sin²θ – 1)
  • 1 /((1-sin²θ)/sin²θ
  • sin²θ/((1-sin²θ)

As we know that 1-sin²θ=cos²θ

  • sin²θ/((1-sin²θ) = sin²θ/cos²θ = tan²θ

according to the QUESTION:

  • tan²θ = 3
  • tanθ = √3

Value of tan is √3 only when θ is 60°

So,

  • tanθ = tan60°

So the value of θ is 60°


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