`a)`

`M = 4\cos^2 45^o + \sqrt{3}\cot 30^o - 16\cos^3 60^o`

`M = 4 . ((\sqrt{2})/(2))^2 + \sqrt{3} . \sqrt{3} - 16 . ((1)/(2))^3`

`M = 4 . (2)/(4) + 3 - 16 . (1)/(8)`

`M = 2 + 3 - 2`

`M = 3`

 Vậy `M = 3`

`b)`

`N = (2\sin 30^o - \sin 60^o)/(\cos^2 30^o - \cos 60^o)`

`N = (2 . (1)/(2) - (\sqrt{3})/(2))/(((\sqrt{3})/(2))^2 - (1)/(2))`

`N = (1 - (\sqrt{3})/(2))/((3)/(4) - (1)/(2))`

`N = (2 - \sqrt{3})/(2): (1)/(4)`

`N = (2 - \sqrt{3})/(2) . 4`

`N = 2(2 - \sqrt{3})`

`N = 4 - 2\sqrt{3}`

Vậy `N = 4 - 2\sqrt{3}`

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