Question

If `cosA/3 = cosB/4 = 1/5, - π/2 < A < 0` and `- π/2 < B < 0`, then the value of 2 sin A + 4 sin B is ______.

विकल्प

• 4

• – 2

• – 4

• 0

Answer 1

If `cosA/3 = cosB/4 = 1/5, - π/2 < A < 0` and `- π/2 < B < 0`, then the value of 2 sin A + 4 sin B is – 4.

Explanation:

Given, cos A = `3/5` and cos B = `4/5`

∵ ∠A and ∠B lie on the IV quadrant.

∴ sin A = `-sqrt(1 - 9/25)` and sin B = `-sqrt(1 - 16/25)`

`\implies` sin A = `-4/5` and sin B = `-3/5`

Now, 2 sin A + 4 sin B = `2(-4/5) + 4(-3/5)`

= `-8/5 - 12/5`

= `-20/5`

= – 4