Find the exact value of the expression dont use a calculator

Find the exact value of the expression, don\'t use a calculator. tan (sin^-1 1/3) cot[sin^-1(-Squareroot 2/3)] sec (sin^-1 2 Squareroot 5/5)

Solution

29). cot [ sin^-1 (-sqrt(2)/3) ]

cot(sin^1(x))=cos(sin^1(x))/sin(sin^1(x))=(1x^2)/x

so plug x = -2 /3

cot(sin^1(x)) = (1-2/9) /-2/3

= 7/-2

= - (7/2)