Question

If 2 cos θ + sin θ = `1(θ ≠ π/2)`, then 7 cos θ + 6 sin θ is equal to ______.

Options

• `1/2`

• 2

• `11/2`

• `46/5`

Answer 1

If 2 cosθ + sinθ = `1(θ ≠ π/2)`, then 7 cosθ + 6 sinθ is equal to 2.

Explanation:

2 cos θ = 1 − sin θ

on squaring both the sides

⇒ 4 cos²θ = sin²θ − 2 sin θ + 1

⇒ 4(1 − sin²θ) = sin²θ − 2 sin θ + 1

⇒ 5 sin²θ − 2 sin θ − 3 = 0

⇒ sin θ = 1; sin θ = `-3/5`

As per the question θ = `pi/2`

hence here sin θ = `-3/5` so the cos θ = `4/5`

required answer = `7 (4/5) + 6 (-3/5) = 2`