Question

If α = `cos^-1(3/5)`, β = `tan^-1(1/3)`, where 0 < α, β < `π/2`, then α – β is equal to ______.

Options

• `sin^-1(9/(5sqrt(10)))`

• `cos^-1(9/(5sqrt(10)))`

• `tan^-1(9/(5sqrt(10)))`

• `tan^-1(9/14)`

Answer 1

If α = `cos^-1(3/5)`, β = `tan^-1(1/3)`, where 0 < α, β < `π/2`, then α – β is equal to `underlinebb(sin^-1(9/(5sqrt(10))))`.

Explanation:

cosα = `3/5`                          tanβ = `1/3`

sin(α – β) = sinαcosβ – cosαsinβ

= `4/5 xx 3/sqrt(10) - 3/5 xx 1/sqrt(10)`

sin(α – β) = `9/(5sqrt(10))`

⇒ α – β = `sin^-1(9/(5sqrt(10)))`