Question

Find value of tan (cos^–1x) and hence evaluate `tan(cos^-1  8/17)`

Answer 1

Let cos^–1x = θ

Then cos θ = x

Where θ ∈ [0, π]

Therefore, tan(cos^–1x) = tan θ

= `sqrt(1 - cos^2 theta)/costheta`

= `sqrt(1 - x^2)/x`.

Hence `tan(cos^-1  8/17)`

= `sqrt(1 - (8/17)^2)/(8/17)`

= `15/8`.