If cosec²θ + cot²θ = 7, then the value of 'θ' when 0° ≤ θ ≤ 90° is:

If cosec²θ + cot²θ = 7, then the value of 'θ' when 0° ≤ θ…

If cosec²θ + cot²θ = 7, then the value of 'θ' when $0° \leq \theta \leq 90°$ is:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e. 30°.

cosec²θ + cot²θ = 7

We know that,

⇒ cosec²θ = 1 + cot²θ

Now,

⇒ 1 + cot²θ + cot²θ = 7

⇒ 1 + 2cot²θ = 7

⇒ 2cot²θ = 6

⇒ cot²θ = 3

⇒ cotθ = $\sqrt3$

⇒ cotθ = cot30°

⇒ θ = 30°