Evaluate the following :
`sin ^(2) ( cos ^(-1) . 1/2) + cos^(2) ( sin^(-1) . 1/3) ` .

Evaluate the following : sin ^(2) ( cos ^(-1) . 1/2) + cos^(2) ( sin^(-1)√3/2 . ) .

Evaluate the following cos [ cos^(-1) ( (-1)/2) - sin^(-1) ( 1/2)] .

For the principal values, evaluate each of the following : (i) cos^(-1) (1/2)+2sin^(-1) (1/2) (ii) cos^(-1)(1/2)-2sin^(-1)(-1/2)

Evaluate following 1. sin(cos^(-1) 3//5) 2. cos(tan^(-1)3//4) 3. sin(pi/2-sin^(-1) (-1/2))

Evaluate the following: sin^(-1)(sin(pi/4)) (ii) cos^(-1)(cos(2pi/3)) tan^(-1)(tan(pi/3))

Evaluate the following. cos^(-1)(-(1)/(2)) +sin^(-1)(-(1)/(2))

Evaluate the following: a) sin^(-1)(sin(pi/4)) b) cos^(-1)(cos(2pi/3)) c) tan^(-1)(tan(pi/3))

Evaluate the following: (i) sin^(-1)(sin(pi/4)) (ii) cos^(-1)(cos(2pi)/3)) tan^(-1)(tan(pi/3))

For the principal values, evaluate each of the following : (i) sin^(-1)(-1/2)+2cos^(-1)(-(sqrt(3))/2) (ii) sin^(-1)(-(sqrt(3))/2)+cos^(-1)((sqrt(3))/2)