Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If α is an acute angle, which of the following options will NOT necessarily be equal to the value of sec α?

Options:

$\frac{1}{cosα}$

$\frac{1}{sinα}$

$\sqrt{1+tan^2α}$

$\frac{tanα}{sinα}$

Correct Answer:

$\frac{1}{sinα}$

Explanation:

We know,

Sec α = \(\frac{1}{cosα}\)

And

sec² α  - tan² α = 1

sec² α = 1 + tan² α

sec α = \(\sqrt {  1 + tan² α }\)

And ,

sec α = \(\frac{1}{cosα}\)

multiply and divide by sinα .

sec α = \(\frac{1}{cosα}\) × \(\frac{sinα}{sinα}\) 

= \(\frac{tanα}{sinα}\)

But 

secα  ≠ \(\frac{1}{sinα}\)