please guide

sin780.sin480+cos240.cos300

I assume that the arguments of the trgonometric functions are in degree(?).

If so:

You are supposed to know that \(\displaystyle \displaystyle{\sin(0^\circ) = \sin(360^\circ)}\)

and therefore

\(\displaystyle \displaystyle{\sin(780^\circ) = \sin(60^\circ) = \frac12 \sqrt{3}}\)

Re-write the arguments of the other values.

You should come out with \(\displaystyle \displaystyle{\frac12}\) as the total result.
 
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