Question

Select the correct option from the given alternatives:

If α is a root of 25cos²θ + 5cosθ – 12 = 0, `pi/2` < α < π, then sin2α is equal to

Options

• `-24/25`

• `-13/18`

• `13/18`

• `24/25`

Answer 1

`-24/25`

Explanation:

25cos²θ + 5cosθ – 12 = 0

∴ (5cosθ + 4) (5cosθ – 3) = 0

∴ cosθ = `-4/5 or costheta = 3/5`

Since `pi/2 < α < pi`,

cos α < 0

∴ cos α = − `4/5`

sin²α = 1 - cos²α = `1 - 16/25 = 9/25`

∴ sin α = `±3/5`

Since `pi/2 < α < pi`,

sin α > 0

∴ sin α = `3/5`

sin 2 α = = 2sin α cos α

= `2(3/5)((-4)/5)`

= `-24/25`