Calculate the expression sin^-1(sin(5pi/3))+tan^-1(tan(2pi/3))?
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We have to determine the value of sin^-1(sin(5pi/3)) + tan^-1(tan(2pi/3))
sin^-1(sin(5pi/3)) or arc sin (sin (5pi/3)) = 5*pi/3
tan^-1(tan(2pi/3)) or arc tan (tan (2pi/3)) = 2*pi/3
Adding 5*pi/3 and 2*pi/3:
5*pi/3 + 2*pi/3 = 7*pi/3
The result of the expression is 7*pi/3
We'll solve the problem based on the following rules:
sin^-1(sin(x)) = arcsin (sin x) = x and arctan(tan x) = x
tan^-1(tan(x)) = arctan(tan x) = x
According to these rules, we'll get:
arcsin (sin (5pi/3)) = 5pi/3
arctan(tan (2pi/3)) = 2pi/3
arcsin (sin (5pi/3)) + arctan(tan (2pi/3)) = 5pi/3 + 2pi/3
arcsin (sin (5pi/3)) + arctan(tan (2pi/3)) = 7pi/3
The values of the given sum of inverse trigonometric functions is 7pi/3.
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