Find the Exact Value

Question

Find the exact value of [sec(pi/4)cos(2pi/3)]/[tan(pi/6)/csc(3pi/4)]. You must have exact values, no decimals. 

Answer 1

[sec(π/4)cos(2π/3)]/[tan(π/6)/csc(3π/4)].

=cos(2π/3)/[cos(π/4)tan(π/6)sin(3π/4)]

=-.5/[(√2/2)(√3/3)√2/2)]=-3/√3=-√3

The only tricky parts are finding the reference angles for

2π/3 and 3π/4