Precalculus: Find exact value of each expression:

Question

Find exact value of each expression:

a) sin(sin^-1 (3/5) - cos^-1 (-4/5)

b) sin(2 sin^-1 (sqrt(3) /2) )

Answer 1

sin(A-B)=sin(A)cos(B)-sin(B)cos(A)

A=sin^-1(3/5),,,,,,A=cos^-1(4//5),,,,,,,B=cos^-1(4/5),,,,,,B=sin^-1(3/5)

sin(A-B)=12/25-12/25=0

sin(2A)=2sin(A)cos(A)

A=sin^-1((√3)/2),,,,,A=cos^-1(1/2)

sin(2A)=2*((√3)/2)*(1/2)

Answer 2

Both are based on basic triangles. Draw and label.