a) (2sin30o+ cos135o – 3tan150o).(cos180o – cot60o)
= (2sin30o+ cos45o – 3tan30o).(cos180o – tan30o)
= $\left ( 2.\frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2} -3\frac{1}{\sqrt{3}}\right )\left ( -1-\frac{1}{\sqrt{3}} \right )$
= $-\frac{\sqrt{6}+3\sqrt{2}}{6}$
b) $sin^{2}90^{o}+cos^{2}120^{o}+cos^{2}0^{o}-tan^{2}60^{o}+cot^{2}135^{o}$
= $sin^{2}90^{o}+ cos^{2}0^{o}+cos^{2}120^{o}-tan^{2}60^{o}+cot^{2}135^{o}$
= 1 + 1 + $ cos^{2}60^{o}-tan^{2}60^{o}+cot^{2}45^{o}$
= 2 + $\frac{1}{4}$ - 3 + 1
= $\frac{1}{4}$
c) cos60o.sin30o + cos230o
= sin30o.sin30o + cos230o
= sin230o + cos230o
= 1