Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If $\sin θ+cosec\,θ = 2$, then what is the value of $\sin^2θ + cosec^2\,θ$?

Options:

4

8

2

16

Correct Answer:

2

Explanation:

sinθ + cosec θ = 2

{ we know, sinθ = \(\frac{1}{sinθ}\) }

sinθ + \(\frac{1}{sinθ}\) = 2

On squaring both side ,

( sinθ + \(\frac{1}{sinθ}\) )² = 2²

 sin²θ + \(\frac{1}{sin²θ}\) + 2  = 4 

 sin²θ + \(\frac{1}{sin²θ}\) = 2