Question

1)sin(a-b)-sin(a+b) 2)sin(30°-a)+cos(60°-a) 3)

Answer 1

$\frac{x}{y} 1)\; \; sin(\alpha -\beta )-sin(\alpha +\beta)=2\cdot sin\dfrac{\alpha-\beta-(\alpha +\beta )}{2}\cdot cos\dfrac{\alpha -\beta+(\alpha +\beta )}{2}=\\\\\\=2\cdot sin(-\beta)\cdot cos\alpha =-2\, sin\beta\cdot cos\alpha \\\\\\2)\; \; sin(30-a)+cos(60-a)=\\\\=sin30\cdot cosa-cos30\cdot sina+cos60\cdot cosa+sin60\cdot sina=\\\\=\dfrac{1}{2}\cdot cosa-\dfrac{\sqrt3}{2}\cdot sina+\dfrac{1}{2}\cdot cosa+\dfrac{\sqrt3}{2}\cdot sina=cosa$

Answer 2

It seems like you've provided incomplete mathematical expressions. Could you please provide the complete expressions you'd like me to help you with? For example, the third expression is missing. If you provide the full expressions, I'd be happy to assist you with simplifying or solving them.