Question

cos18 ∘ ⋅cos72 ∘ −sin63 ∘ ⋅cos27 =-0.5​

Answer 1

$\cos 18^{\circ} \cos 72^{\circ}-\sin 63^{\circ} \cos 27^{\circ}=-0,5\\\sin 72^{\circ} \cos 72^{\circ}-\sin 63^{\circ} \sin 63^{\circ}=-0,5\\ \sin 72^{\circ} \cos 72^{\circ}=\sin^2 63^{\circ}-0,5\\2 \sin 72^{\circ} \cos 72^{\circ}=2\sin^2 63^{\circ}-1\\2 \sin 72^{\circ} \cos 72^{\circ}=2\cos^2 27^{\circ}-1\\\sin 144^{\circ}=\cos 54^{\circ}\\\sin 36^{\circ}=\cos 54^{\circ}\\\sin 36^{\circ}=\sin 36^{\circ}\\1=1$