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31 votes
31 votes
What is the exact value of
(cos(tan^(-1) (-1)) )/(sin(cos^(-1)((√(3))/(2))))

Enter your answer, as a simplified fraction, in the box


(cos(tan^(-1) (-1)) )/(sin(cos^(-1)((√(3))/(2)))) =

User Sfackler
by
2.3k points

1 Answer

18 votes
18 votes

We have

arctan(-1) = -π/4

cos(-π/4) = 1/√2

and

arccos(√3/2) = π//6

sin(π/6) = 1/2

Then

cos(arctan(-1)) / sin(arccos(√3/2)) = (1/√2) / (1/2) = √2

User Swanand Taware
by
3.0k points