Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If $sec^2 θ=\frac{4}{3}$, then the value of $ cosec (θ + 30^o)$ is _________. [ θ is the acute angle.]

Options:

$-\frac{2}{\sqrt{3}}$

$\frac{2}{\sqrt{3}}$

$\frac{1}{\sqrt{3}}$

$-\frac{1}{\sqrt{3}}$

Correct Answer:

$\frac{2}{\sqrt{3}}$

Explanation:

sec²θ = \(\frac{4}{3}\)

secθ = \(\frac{2}{√3}\)

{ we know, sec30º = \(\frac{2}{√3}\) }

So, θ = 30º 

Now,

cosec ( θ + 30º )

= cosec ( 60º ) 

= \(\frac{2}{√3}\)