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))/(…

Question

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))))` =

Answer 1

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