Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

What is $\sqrt{(1-sinA)}\sqrt{(1+sinA)}$?

Options:

$sec^2A$

secA + tanA

$tan^2A$

cosA

Correct Answer:

cosA

Explanation:

 $\sqrt{(1-sinA)}\sqrt{(1+sinA)}$

= $\sqrt{1 - sin^2A}$               (1 - sin²A = cos²A)

= $\sqrt{cos^2A}$

= cosA 

Alternatively, 

take A = 45°

 $\sqrt{(1-sinA)}\sqrt{(1+sinA)}$

=  $\sqrt{(1-sin45)}\sqrt{(1+sin45)}$

=  $\sqrt{(1-\frac{1}{\sqrt{2}})}\sqrt{(1+\frac{1}{\sqrt{2}})}$

= $\frac{1}{\sqrt{2}}$

= cosA