Ta có:

a) 

$A = sin45^{o} + 2sin60^{o} + tan120^{o} + cos135^{o}$

$A = \frac{1}{\sqrt{2}} + 2.\frac{\sqrt{3}}{2} + -\sqrt{3} - \frac{1}{\sqrt{2}}$

$A = 0$

b) 

$B = tan45^{o} . cot135^{o} - sin30^{o} . cos120^{o} - sin60^{o} . cos150^{o}$

$B = 1 . (-1) - \frac{1}{2} . \frac{1}{2} - \frac{\sqrt{3}}{2} . (-\frac{\sqrt{3}}{2})$

$B = 0$

c) 

$C = cos^{2}5^{o} + cos^{2}25^{o} + cos^{2}45^{o} + cos^{2}65^{o} + cos^{2}85^{o}$

Vì $ 5^{o} = 90^{o} - 85^{o}, 25^{o} = 90^{o} - 65^{o}$

Ta có: 

$cos5^{o} = sin45^{o}, cos^{2}25^{o} = sin65^{o}$

$C = (sin^ {2}85^{o} + cos^{2}85^{o}) + (sin^ {2}65^{o} +  cos^{2}65^{o}) + cos^{2}45^{o}$

$C = 1 + 1 + \frac{1}{2}$ 

$C = \frac{5}{2}$

d) 

$D = \frac{1}{1 + tan^{2}73^{o}} - 4tan75^{o} . cot105^{o} + 12sin^{2}107^{o} - 2tan40^{o} . cos60^{o} . tan50^{o};$

Vì $73^{o} + 107^{o} = 75^{o} + 105^{o} = 100^{o}$

Ta có:

(1)$ \frac{1}{1 + tan^{2}73^{o}} + 12sin^{2}107^{o} = 12(cos^{2}73^{o} + sin^{2}73^{o} = 12$

(2) $tan75^{o} . cot105^{o} = tan75^{o} . (-cot75^{o}) = -1$

Vì$ 40^{o} + 50^{o} = 90^{o}$

Ta có:

(3) $tan40^{o} . tan50^{o} = tan40^{o} . cot40^{o}$

Từ (1), (2) và (3) =>$ D = 12 - 4 . (-1) - 2 . 1 . \frac{1}{2} = 15$

e) 

$E = 4tan32^{o} . cos60^{o} . cot148^{o} + \frac{5cot^{2}108^{o}}{1 + tan^{2}18^{o}} + 5sin^{2}72^{o}$

Vì $148^{o} + 32^{o} = 108^{o} + 72^{o} = 180^{o}$

Và $72^{o} + 18^{o} = 90^{o}$

Nên $E = 4tan32^{o} . (-cot32^{o}) . cos60^{o} + 5(-cot72^{o})^{2} .  cos^{2}18^{o} + 5cos^{2}18^{o}$

$E = 4 . (-1) . \frac{1}{2} + 5 . 1 = 3$