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Find the values of x in [0,2pi] for whic...

Find the values of `x in [0,2pi]` for which function `f(x) = tan^(-1) (tan x) and g(x) = cos^(-1) (cos x)` are identical

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The correct Answer is:
`[0, pi//2) uu {2pi]`
Let us draw the graph of both th efunction for `x in [0, 2pi]`

In the above figure, graph of `y = f (x) and y = g (x)` coincide for `x in [0,pi//2) uu {2pi}`
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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
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  18. Solve 2 cos^(-1) x + sin^(-1) x = (2pi)/(3)

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  19. Prove that sin^(-1) cos (sin^(-1) x) + cos^(-1) x = (pi)/(2), |x| le 1

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