Prove that: `sin780^0sin 120^0+cos 240^0sin390^0=1/2`

Explanation

`Sin 780^{circ} cdot Sin 120^{circ}+Cos 240^{circ} cdot Sin 390^{circ}=frac{1}{2}`


Taking `LHS`


`Sin 780^{circ} cdot Sin 120^{circ}+Cos 240^{circ} cdot Sin 390^{circ}`


`Rightarrow Sin(2 times 360^{circ}+60^{circ}) cdot Sin(180^{circ}-60^{circ})+Cos(180^{circ}+60^{circ}) cdot Sin(360^{circ}+30^{circ})`


`=>Sin(4 pi+60^{circ}) cdot Sin(pi-60^{circ})+Cos(pi+60^{circ}) cdot Sin(2 pi+30^{circ})`


`Rightarrow Sin^{circ} 0^{circ} cdot Sin 60^{circ}-Cos 60^{circ} cdot Sin 30^{circ}`



`Rightarrow frac{sqrt{3}}{2} cdot frac{sqrt{3}}{2}-frac{1}{2} cdot frac{1}{2}=frac{3}{4}-frac{1}{4}`


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