Question

If \(cosec \theta + \cot \theta = 2, then \sin \theta\) is:
1. \(\frac{4}{5}\)
2. \(\frac{2}{5}\)
3. \(\frac{3}{5}\)
4. \(\frac{3}{4}\)

Answer 1

Correct Answer - Option 1 : \(\frac{4}{5}\)

Given : 

cosec θ + cot θ = 2 

Formula used :

cosec²θ - cot²θ = (cosec θ + cot θ)(cosec θ - cot θ) = 1 

Calculations :

cosec θ + cot θ = 2       ....(1)

cosec θ - cot θ = 1/2     ....(2)

Solving equation 1 and 2 , we get 

cosec θ = 5/4 

⇒ sinθ = 4/5           (sin θ = (1/cosec θ)

∴ sin θ is equal to 4/5.