Question

If `θ∈[(5π)/2, 3π]` and 2cosθ + sinθ = 1, then the value of 7cosθ + 6sinθ is ______.

Options

• 4.00

• 5.00

• 6.00

• 7.00

Answer 1

If `θ∈[(5π)/2, 3π]` and 2cosθ + sinθ = 1, then the value of 7cosθ + 6sinθ is 6.00.

Explanation:

2cosθ + 1 – sinθ

4cos²θ = 1 + sin²θ – 2sinθ

4 – 4sin²θ = 1 + sin²θ – 2sinθ

5sin²θ – 2sinθ – 3 = 0

(5sinθ + 3)(sinθ – 1) = 0

sinθ = 1, as `θ∈[(5π)/2, 3π]`

So, cosθ = 0

Now, 7cosθ + 6sinθ = 6