First slide

Introduction to ITF

Question

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

Moderate

A

$\frac{17 π}{42} - 2$
B

$- 2$
C

$- \frac{π}{21} - 2$
D

$\frac{π}{21}$

Solution

$W e h a v e \sin^{- 1} (\sin \frac{22 π}{7}) + \cos^{- 1} (\cos \frac{5 π}{3}) + \tan^{- 1} (\tan \frac{5 π}{7}) + \sin^{- 1} (\cos 2) = \sin^{- 1} (\sin (3 π + \frac{π}{7})) + \cos^{- 1} (\cos (2 π - \frac{π}{3})) + \tan^{- 1} (\tan (π - \frac{2 π}{7})) + \sin^{- 1} (\sin (\frac{π}{2} - 2)) = - \frac{π}{7} + \frac{π}{3} - \frac{2 π}{7} + \frac{π}{2} - 2 = \frac{17 π}{42} - 2$

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