SSC CHSL 2024 PYQ — Question 63

The correct answer is option 2 i.e. $\frac{2xy}{x^2-y^2}$.

Given that

If $sin\theta=\frac{2xy}{x^2+y^2}$,

Sin $\theta$ = Perpendicular/Hypontaneous = 2xy/(x² + y²)

Formula used

By using Pythagoras' theorem

 a² + b² = c²

where, a = base, b = perpendicular, c = Hypontaneous

(x² + y²)² = (2xy)² + a²

⇒ a² = x⁴ + y⁴ + 2x² y² - 4x² y²

⇒ a² = x⁴ + y⁴ - 2x² y² = (x² - y²)²

⇒ a = (x² - y²)

Hence, tan $\theta$ =  Perpendicular/Base = 2xy/(x² - y²)