If 3sin θ + 5cos θ = 4, then what is the value of (3cos θ – 5sin θ)2?
If 3sin θ + 5cos θ = 4, then what is the value of (3cos θ – 5sin θ)2? Correct Answer 18
Given, (3sin θ + 5cos θ) = 4
Squaring both sides,
⇒ (3sin θ + 5cos θ)2 = 42
⇒ 9sin2 θ + 25cos2 θ + 30sin θ cos θ = 16
⇒ 30sin θ cos θ = 16 – 9sin2 θ – 25cos2 θ ----(1)
Now,
(3cos θ – 5sin θ)2
= 9cos2 θ + 25sin2 θ – 30sin θ cos θ
= 9cos2 θ + 25sin2 θ – 16 + 9sin2 θ + 25cos2 θ
= 34(sin2 θ + cos2 θ) – 16
= 34 – 16
= 18
মোঃ আরিফুল ইসলাম
Feb 20, 2025