Find the exact values of the following expressions Do not us

Find the exact values of the following expressions. Do not use a calculator. sin^-1(sin 2pi/3) sec(arc cos 2/3) sim(2 tan^-1(3/5))

sec(cos^-12/3)

Let cos^-12/3=t

cos t = 2/3

Sec t = 1/cos t= 3/2

Therefore sec(cos^-12/3)= 3/2

c. sin(2 tan^-13/5)

tan^-13/5=t

tan t= 3/5

Opposite=3 and adjacent=5

Hypotenuse= sqrt(25+9) = sqrt 34

Sin t= 3/sqrt34 cos t= 5/sqrt34

Sin 2t= 2sin t cos t= 15/17

Therefore sin(2tan^-13/5)= 15/17