If sin^-1 x + sin^-1 y = 2 pi / 3 , then find the value of cos ^-1 x + cos ^-1 y .
(sin^-1 = sine inverse )
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sin^-1 x + cos^-1 x = pi/2
sin^-1 x = pi/2 - cos^-1 x
sin^-1 x + sin^-1 y = 2pi/3
pi/2 - cos^-1 x + pi/2 - cos^-1 y = 2pi/3
-(cos^-1 x + cos^-1 y) = 2pi/3 - pi
cos^-1 x + cos^-1 y = pi/3
sin^-1 x = pi/2 - cos^-1 x
sin^-1 x + sin^-1 y = 2pi/3
pi/2 - cos^-1 x + pi/2 - cos^-1 y = 2pi/3
-(cos^-1 x + cos^-1 y) = 2pi/3 - pi
cos^-1 x + cos^-1 y = pi/3
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