Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If $\frac{cosθ+sinθ}{cosθ-sinθ}=8$, then the value of cot θ is equal to :

Options:

$\frac{6}{5}$

$\frac{9}{7}$

$\frac{8}{7}$

$\frac{7}{6}$

Correct Answer:

$\frac{9}{7}$

Explanation:

\(\frac{cosθ + sinθ }{cosθ - sinθ }\) = 8

By applying Dividendo and Componendo

\(\frac{cosθ + sinθ + cosθ - sinθ }{cosθ + sinθ - cosθ + sinθ }\) =  \(\frac{8+1 }{8-1}\)

\(\frac{cosθ  }{ sinθ  }\) =  \(\frac{9 }{7}\)

cot θ = \(\frac{9 }{7}\)