m2 trigonometric functions

1. in triangle ABC, if sinA=cosB-cosC, prove that triangle ABC is a right-angled triangle.
2. if A+B+C= 180degree and sinA=(sinB+sinC), prove that cot(B/2)cot(C/2)=3
3.GIVEN THAT cos3a+cos3b+cos3c=1-4sin((3a)/2)sin((3c)/2)sin((3b)/2)
in triangle xyz, prove that one of the angles of the triangle is 120degree if cos3x+cos3y+cos3z=1