Prove that: `sin 12^0sin 48^0sin 54^0=1/8dot`

Explanation

`=frac{1}{2}(2 sin 12^{circ} sin 48^{circ}) sin 54^{circ}`


`=frac{1}{2}[cos (36^{circ})-cos (60^{circ})] sin 54^{circ}`


`=frac{1}{2}(cos 36^{circ}-frac{1}{2}) sin 54^{circ}`


`=frac{1}{4}(2 cos 36^{circ} sin 54^{circ}-sin 54^{circ})`


`=frac{1}{4}(sin 90^{circ}+sin 18^{circ}-sin 54^{circ})`


`=frac{1}{4}(1+frac{sqrt{5}-1}{4}-frac{sqrt{5}+1}{4})`


`=frac{1}{4}(1+frac{sqrt{5}-1-sqrt{5}-1}{4}(1-frac{1}{2})=frac{1}{8}.`