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If A = 60 B= 30 prove sin (a-b) =sin a cos b - cos a sin b

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Given \ A= 60 \ and \ B=30\\\\we \ have \ to \ prove \ sin (a-b) =sin \ a \ cos \ b - cos \ a sin \ b\\\\We \ know \ that \ sin \ 30=\frac{1}{2} \ sin \ 60=\frac{\sqrt{3} }{2} \ and \ cos \ 30=\frac{\sqrt{3} }{2} \ cos \ 60=\frac{1}{2}\\\\putting \ value \ here\\\\sin (a-b) =sin \ a \ cos \ b - cos \ a \ sin \ b\\\\sin(60-30)=sin \ 60 \times cos \ 30-cos \ 60 \times sin \ 30\\\\sin \ 30=sin \ 60 \times cos \ 30-cos \ 60 \times sin \ 30\\\\\\\frac{1}{2}=\frac{\sqrt{3} }2} \times \frac{\sqrt{3} }2}-\frac{1}{2} \times \frac{1}{2}\\\\\frac{1}{2}=\frac{3}{4}-\frac{1}{4}\\\\ \frac{1}{2}=\frac{3-1}{4}\\\\\frac{1}{2}=\frac{2}{4}\\\\\frac{1}{2}=\frac{1}{2}\\\\Hence \ proved.

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