Cos 150° + sin 45° + ½ cotg(-330°) = A. ½√3. D. -½√2 B. -½√3. E. √2 C. ½√2

cos 150° + sin 45° + 1/2 cot (-330°)
= cos (180° - 30°) + sin 45° + 1/2 (- cot 330°)
= - cos 30° + sin 45° - 1/2 cot (360° - 30°)
= - cos 30° + sin 45° - 1/2 (- cot 30°)
= - 1/2 √3 + 1/2 √2 - 1/2 . -√3
= -1/2 √3 + 1/2 √2 + 1/2 √3
= 1/2 √2

[tex]\cos 150^{\circ}=\cos (180-30)^{\circ}\\\cos 150^{\circ}=-\cos 30^{\circ}\\\cos 150^{\circ}=- \frac{1}{2} \sqrt{3} \\\\\sin45^{\circ}= \frac{1}{2} \sqrt{2} \\\\ \frac{1}{2} \cot(-330)^{\circ}=\frac{1}{2} \cot(30)^{\circ}\\\ \frac{1}{2} \cot(-330)^{\circ}= \frac{1}{2} \sqrt{3} \\\\\text{Kemudian dijumlahkan, sehingga}\\- \frac{1}{2} \sqrt{3} + \frac{1}{2} \sqrt{2}+ \frac{1}{2} \sqrt{3} = \frac{1}{2} \sqrt{2} } \\\\\boxed{\boxed{\text{C. }\frac{1}{2} \sqrt{2} } }}[/tex]