Cos^-1(cos5π/3)+sin^-1(cos5π/3)is?

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Answer 1 · 2018-04-13T17:41:03

# pi/2#.

Recall that, #cos^-1x+sin^-1x=pi/2, |x| le1#.

Letting #x=cos5pi/3," and noting that "|cos(5pi/3)| le 1#,

we have,

#cos^-1(cos(5/3pi))+sin^-1(cos(5/3pi))=pi/2#.

Otherwise, we have,

#cos(5pi/3)=cos(2pi-pi/3)=cos(pi/3)=1/2#.

#:. cos^-1(cos(5pi/3))=cos^-1(1/2)=pi/3#, and,

#sin^-1(cos(5pi/3))=sin^-1(1/2)=pi/6#.

Adding, we get #pi/2#, as the Answer.