If (sinθ)/x = (cosθ)/y then sin θ - cosθ is:

If $\frac{\sin\theta}{x} = \frac{\cos\theta}{y}$ then $\sin \theta - \cos\theta$ is:

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. $\frac{x-y}{\sqrt{x^2+y^2}}$ .

Let $\frac{\sin \theta}{x} = \frac{\cos \theta}{y} = k$

⇒ sinθ = kx

⇒ cosθ = ky

sin²θ + cos²θ = 1

⇒ k²(x² + y²) = 1

⇒ $k^2 = \frac{1}{x^2 + y^2}$

⇒ $k = \frac{1}{x^2 + y^2}$

sinθ - cosθ = kx - ky

= k(x - y)

$= \frac{x - y}{\sqrt{x^2 + y^2}}$

SSC CGL 2026 PYQ — Question 23