Question

If `π/2 < α < π, π < β < (3π)/2`; sin α = `15/17` and tan β = `12/5`, then the value of sin(β – α) is ______.

Options

• `-171/221`

• `-21/221`

• `21/221`

• `171/221`

Answer 1

If `π/2 < α < π, π < β < (3π)/2`; sin α = `15/17` and tan β = `12/5`, then the value of sin(β – α) is `underlinebb(171/221)`.

Explanation:

Given, sin α = `15/17`, tan β = `12/5`

`\implies` cos α = `8/17`, sin β = `12/13` and cos β = `-5/13` 

`\implies π < β < (3π)/2`

∴ cos β = `-5/13`

sin(β – α) = sin β cos α – cos β sin α = `171/221`