If $cos \theta = \frac{4x}{1+4x^2}$, the

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If $cos \theta = \frac{4x}{1+4x^2}$, then what is the value of sin θ ?

Options:

$\frac{1+4x^2}{1-4x^2}$

$\frac{1+4x^2}{4x^2}$

$\frac{1-4x^2}{1+4x^2}$

$\frac{1-4x^2}{4x}$

Correct Answer:

$\frac{1-4x^2}{1+4x^2}$

Explanation:

cosθ = $\frac{4x}{1 + 4x²}$

{ cosθ = $\frac{B}{H}$ }

Using pythagoras theorem,

P² + B² = H²

P² + (4x)² = (1+4x²)²

P² = 1 + 16x4 + 8x² - 16x² = ( 1 - 4x² )²

P = 1 - 4x²

Now,

sinθ

= $\frac{P}{H}$

= $\frac{ 1 - 4x² }{1+4x²}$