# Evaluate. Q.2. Using principal values, evaluate the following.${\mathrm{cos}}^{-1}\left(\mathrm{cos}\frac{2\mathrm{\pi }}{3}\right)+{\mathrm{sin}}^{-1}\left(\mathrm{sin}\frac{2\mathrm{\pi }}{3}\right)$.

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I too got the same answer but in back its written as "pi" is the required answer. :/ Thats why I got confused. Is it possible that the back page answer is wrong? I think so. Thanks :D

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cos^-1(cos(2π/3)) + sin^-1(sin(2π/3) = 2π/3 + sin^-1(sin(π-π/3)) (This is because principal value branch of cos^-1 lies in [0,π] while that of sin^-1 lies in [-π/2,π/2]) = 2π/3 + sin^-1(sin(π/3)) = 2π/3 + π/3 = 3π/3 = π P.S. It coincides with the answer at the back of your textbook! Sorry if the answer is not formatted. That's the fault of meritnation website.
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