Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

$\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}} + \sqrt{\frac{1 - \cos \theta}{1 + \cos \theta}}$ = ________.

Options:

2 sin θ

2 cos θ

2 cosec θ

2 sec θ

Correct Answer:

2 cosec θ

Explanation:

$\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}} + \sqrt{\frac{1 - \cos \theta}{1 + \cos \theta}}$

= $\sqrt{\frac{(1 + \cos \theta)(1 - \cos \theta)}{(1 - \cos \theta)(1 - \cos \theta)}} + \sqrt{\frac{(1 - \cos \theta)(1 + \cos \theta)}{(1 + \cos \theta)(1 + \cos \theta)}}$

= \(\frac{1 - cos θ}{sinθ}\)  + \(\frac{1 + cos θ}{sinθ}\)

= \(\frac{2}{sinθ}\)  = 2cosecθ