How do you find the exact value of the expression ${sin 330}^{\circ} {cos 30}^{\circ} - {cos 330}^{\circ} {sin 30}^{\circ}$ $sin330^circcos30^circ-cos330^circsin30^circ$ ?

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Answer 1 · 2017-01-04T06:36:46

${sin 330}^{\circ} {cos 30}^{\circ} - {cos 330}^{\circ} {sin 30}^{\circ} = - \frac{\sqrt{3}}{2}$ $sin330^@cos30^@-cos330^@sin30^@=-sqrt3/2$

We can use the identity $sin (A - B) = sin A cos B - cos A sin B$ $sin(A-B)=sinAcosB-cosAsinB$

Hence observe that if $A = 330^{\circ}$ $A=330^@$ and $30^{\circ}$ $30^@$

${sin 330}^{\circ} {cos 30}^{\circ} - {cos 330}^{\circ} {sin 30}^{\circ}$ $sin330^@cos30^@-cos330^@sin30^@$

= $sin (330^{\circ} - 30^{\circ})$ $sin(330^@-30^@)$

= ${sin 300}^{\circ}$ $sin300^@$

And as $sin (360^{\circ} - x) = - sin x$ $sin(360^@-x)=-sinx$

${sin 300}^{\circ} = sin (360^{\circ} - 60^{\circ}) = - {sin 60}^{\circ} = - \frac{\sqrt{3}}{2}$ $sin300^@=sin(360^@-60^@)=-sin60^@=-sqrt3/2$

How do you find the exact value of the expression sin330∘cos30∘−cos330∘sin30∘sin330^circcos30^circ-cos330^circsin30^circ?