Nilai dari cos 105° - cos 45° / sin 105 - sin 15° adalah..

[tex]\frac{\cos{105^{o}}-\cos{45^{o}}}{\sin{105^{o}}-\sin{15^{o}}}=\frac{-2\sin{\frac{105+45}{2}}\sin{\frac{105-45}{2}}}{2\cos{\frac{105+15}{2}}\sin{\frac{105-15}{2}}}=\frac{-2\sin{75}\sin{30}}{2\cos{60}\sin{45}}=-\frac{\sin{75}}{\sin{45}}=-\frac{\sin{(45+30)}}{\sin{45}}=-\frac{\sin{45}\cos{30}+\sin{30}\cos{45}}{\sin{45}}=-(\cos{30}+\sin{30})=-\frac{1}{2}(\sqrt{2}+1)[/tex]