If [1/(1 + cosec θ) - 1/(1 - cosecθ)]cosθ = 2, 0° Sin²θ + cot²θ + sec²θ is:

If [1/(1 + cosec θ) - 1/(1 - cosecθ)]cosθ = 2, 0° Sin²θ +…

If [1/(1 + cosec θ) - 1/(1 - cosecθ)]cosθ = 2, 0° < θ < 90°, then the value of Sin²θ + cot²θ + sec²θ is:

Show answer & explanation

Correct answer: C

Explanation

Correct Answer is option 3 i.e. 7/2

Understanding

Application

We need to solve it by value putting method.

[1/(1 + cosec θ) - 1/(1 - cosecθ)]cosθ = 2, 0° < θ < 90°

Putting θ = 45

⇒ [1/(1 + √2) - 1/(1 - √2)]1/√2

⇒ [(1 - √2 – 1 - √2)/√2]

⇒ 2

Hence, it satisfies the equation.

Now,

Sin²θ + cot²θ + sec²θ

θ = 45

⇒ 1/2 + 1 + 2

⇒ 7/2