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

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Answer 1 · 2015-12-02T20:05:59

$sin(60^@)$

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 $sin(60^@)$

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