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