Find the maximum value of (19 sin θ + 6 cot θ sin θ).

Question

Question

This question was previously asked in

SSC CPO 2024 Official Paper-I (Held On: 27 Jun, 2024 Shift 3)

Answer 1

Given:

Expression: 19 sin θ + 6 cot θ sin θ

Formula used:

The maximum value of an expression of the form a sin θ + b cos θ is √(a² + b²).

Calculations:

Let y = 19 sin θ + 6 cot θ sin θ

We know cot θ = cos θ / sin θ

Substituting, y = 19 sin θ + 6 (cos θ)

Here, a = 19 and b = 6

Maximum value = √(19² + 6²)

⇒ √(361 + 36) = √397

∴ The maximum value of (19 sin θ + 6 cot θ sin θ) is √397.