Question

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

cos (tan^–1 (3x – 1))

Answer 1

cos (tan^–1 (3x – 1)) = `cos["opp"/"Hyp"]`

Let θ = tan^–1(3x – 1)

tan θ = 3x – 1

1 + tan²θ = 1 + (3x – 1)²

sec²θ = 9x² – 6x + 2

sec θ = `sqrt(9x^2- 6x + 2)`

cos θ = `1/sqrt(9x^2 - 6x + 2)`

⇒ cos (tan^–1(3x – 1)) = `1/sqrt(9x^2 - 6x + 2)`