Evaluate the following :
`sin(pi/2 -sin^(-1)(-sqrt3/2))`

Evaluate the following sin(pi/2-sin^(-1)(1/2))

Evaluate the following : cos(cos^(-1)(sqrt3/2)+pi/6)

Find sin(pi/3-sin^(-1)(-1/2)) =

Evaluate the following: int_(-pi/2)^(pi/2)sin^7xdx

Evaluate the following integrals: int_0^(pi/4) sin2xdx

Evaluate the following integrals: int_0^(pi/4) sin^3 2t cos 2t dt

Evaluate the following integrals: int_0^pi sin^2 (x/2) - cos^2(x/2) dx

Solve the following sin^-1x+sin^-1 2x=pi/3

Using properties evaluate the following definite integrals, evaluate the following: int_(-pi/2)^(pi/2) sin^2x dx

Prove the following : (9pi)/8-9/4 sin^(-1)(1/3)=9/4 sin^(-1) ((2sqrt2)/3)