tentukanlah nilai dari Sin 75 derajat cos 15 derajat dikurang cos 75 derajat sin 150 derajat

sin 75 cos 15 - cos 75 sin 150

sin (30 + 45) cos (45 - 30) - cos (30 + 45) sin
{(sin 30 cos 45 + cos 30 sin 45)(cos 45 cos 30 + sin 45 sin 30)} - {(cos 30 cos 45 - sin 30 sin 45) 1/2}

{(√2/4 + √6/4})(√6/4 + √2/4)} - {(√6/4 - √2/4) 1/2}

{√12/16 + 2/16 + 6/16 + √12/16} - {√6/8 - √2/8}

√12/8 + 8/16 - √6/8 - √2/8
1/2 + 2√3/8 - √6/8 - √2/8
1/2 + 1/8 (2√3 - √6 - √2)

#semoga membantu

[tex]\sin{(75^{\circ})}\cos{(15^{\circ})}-\cos{(75^{\circ})}\sin{(150^{\circ})}\\=\cos{(15^{\circ})}\cos{(15^{\circ})}-\sqrt{\frac{\cos{(2\times 15^{\circ})+1}}{2}}\times\sin{(30^{\circ})}\\=\cos^2{(15^{\circ})}-\sqrt{\frac{\cos{(30^{\circ})}+1}{2}}\times \frac{1}{2}\\=2\cos{(30^{\circ})}-1-\sqrt{\frac{\frac{\sqrt{3}}{2}+1}{2}}\times\frac{1}{2}\\=2\times\frac{\sqrt{3}}{2}-1-\sqrt{\frac{1}{2}\times\frac{\sqrt{3}+2}{2}}\times\frac{1}{2}\\=\sqrt{3}-1-\frac{\sqrt{\sqrt{3}+1}}{2}\times\frac{1}{2}[/tex]

[tex]=\sqrt{3}-1-\frac{\sqrt{\sqrt{3}+1}}{4}[/tex]