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Question
Find the value of the expression in terms of x, with the help of a reference triangle
cos (tan–1 (3x – 1))
Solution
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)`
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