Question

Find the value of the expression in terms of x, with the help of a reference triangle

`tan(sin^-1(x + 1/2))`

Answer 1

Let θ = `tan(sin^-1(x + 1/2))`

⇒ sin θ = `x + 1/2`

1 – sin²θ = `1 - (x + 1/2)^2`

cos²θ = `1 - x^2 + x - 1/4`

cos²θ = `3/4 + x - x^2`

cos²θ = `(3 + 4x - 4x^2)/4`

cos θ = `sqrt(3 + 4x + 4x^2)/2`

tan θ = `((x + 1/2) xx 2)/sqrt(3 + 4x + 4x^2)`

tan θ = `(2x + 1)/sqrt(3 + 4x - 4x^2)`