Question

How do you find the exact value of the expression `sin330^circcos30^circ-cos330^circsin30^circ`?

Answer 1

`sin330^@cos30^@-cos330^@sin30^@=-sqrt3/2`

Explanation:

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

Hence observe that if `A=330^@` and `30^@`

`sin330^@cos30^@-cos330^@sin30^@`

= `sin(330^@-30^@)`

= `sin300^@`

And as `sin(360^@-x)=-sinx`

`sin300^@=sin(360^@-60^@)=-sin60^@=-sqrt3/2`