Question

Trigonometry problem.
Please show your solution and explain it. thank you !!

Answer 1

Cute one!

Summarizing:
sec(acot(tan(asin(sin(pi/3)))) .... use asin(sin(x))=x
=sec(acot(tan(pi/3)))
=sec(acot(sqrt(3))) ......... use acot(x)=atan(1/x)
=sec(atan(1/sqrt(3)))
=sec(atan(sqrt(3)/3)) .... evaluate atan(sqrt(3)/3), use unit circle
=sec(pi/6)
=1/cos(pi/6)...... evaluate cos(pi/6), use unit circle
=1/(sqrt(3)/2)
=2/sqrt(3) .... now rationalize
=2sqrt(3)/3