If sec θ + tan θ =

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If sec θ + tan θ = p ; (p > 1) ; then value of \(\frac{cosec θ + 1}{cosec θ - 1}\) is?

Options:

2p + 1

\(\frac{p}{2p + 1}\)

p²

1 - 2p

Correct Answer:

p²

Explanation:

Put p = 3

sec θ + tan θ = 3

sec θ - tan θ = \(\frac{1}{3}\)

⇒ 2sec θ = \(\frac{10}{3}\) ⇒ sec θ = \(\frac{5}{3}\)

then cosec θ = \(\frac{5}{4}\)

\(\frac{cosec θ + 1}{cosec θ - 1}\) = \(\frac{\frac{5}{4} + 1}{\frac{5}{4} - 1}\) = 9 or p²