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