Question

How do you simplify `sin 175˚ cos 55˚ - cos 175˚ sin 55˚`?

Answer 1

`sin(60^@)`

Explanation:

Your expression is in the form

`sin(a)cos(b)-sin(b)cos(a)`, which is exactly the expansion for `sin(a-b)`

So, it must be

`sin(175^@)cos(55^@) - sin(55^@)cos(175^@)=sin(175^@-55^@) = sin(120^@)`

And since `120=180-60` and `sin(180^@-x)=sin(x)`, you can futher simplify the expression into `sin(60^@)`