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Question
What is the value of cos−1 `(cos (2x)/3)+sin^-1(sin (2x)/3)?`
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Solution
`cos^-1(cos (2x)/3)+sin^-1(sin (2x)/3)`
`cos^-1(cos (2x)/3)+sin^-1{sin(pi/3)}` `[because "Range of sine is"[-pi/2, pi/2]; pi/3in [-pi/2,pi/2] "and range of cosine is" [0,pi] ; (2pi)/3in [0, pi]]`
`=(2pi)/3+pi/3`
= π
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