Question

If cosec θ – cot θ = 2, then find the value of cosec² + cot² θ is ______.

Answer 1

If cosec θ – cot θ = 2, then find the value of cosec² + cot² θ is `underlinebb(17/8)`.

Explanation:

Given cosec θ – cot θ = 2.

Using (cosec θ – cot θ)(cosec θ + cot θ) = 1, we get

cosec θ + cot θ = `1/2` 

Let P = cosec θ · cot θ and S = cosec² θ + cot² θ. 

Squaring the two equations:

S – 2P = 4    ...(From (cosec – cot)² = 4) 

S + 2P = `1/4`   ...`("From" ("cosec" + cot)^2 = (1/2)^2)` 

Add them: 2S = `4 + 1/4 = 17/4` 

So S = `17/8`.