If sin θ + cos θ = x; what i

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If sin θ + cos θ = x; what is the value of sinθ.cosθ ?

Options:

\(\frac{1}{2}\)(x² - \(\frac{1}{x^2}\))

\(\frac{1}{4}\)(x² - \(\frac{1}{x^2}\))

Correct Answer:

\(\frac{1}{4}\)(x² - \(\frac{1}{x^2}\))

Explanation:

sin θ + cos θ = x

⇒sin θ - cos θ = \(\frac{1}{x}\)

4sinθ.cosθ = (sinθ + cosθ)² - (sinθ - cosθ)²

⇒ 4sinθ.cosθ = x² - \(\frac{1}{x^2}\)

⇒ sinθ.cosθ = \(\frac{1}{4}\)(x² - \(\frac{1}{x^2}\))