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The value of the expression $\sin^{- 1} (\sin \frac{22 π}{7}) + \cos^{- 1} (\cos \frac{5 π}{3}) + \tan^{- 1} (\tan \frac{5 π}{7}) + \sin^{- 1} (\cos 2)$ is

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17π42−2

-2

−π21−2

π21

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detailed solution

Correct option is A

We have sin-1sin22π7+cos-1cos5π3+tan-1tan5π7+sin-1cos2 =sin-1(sin(3π+π7))+cos-1cos2π-π3+tan-1tanπ-2π7+sin-1sinπ2-2 =-π7+π3-2π7+π2-2 =17π42-2

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The value of the expression sin−1(sin22π7)+cos−1(cos5π3)+tan−1(tan5π7)+sin−1(cos2) is

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The value of the expression $\sin^{- 1} (\sin \frac{22 π}{7}) + \cos^{- 1} (\cos \frac{5 π}{3}) + \tan^{- 1} (\tan \frac{5 π}{7}) + \sin^{- 1} (\cos 2)$ is