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a, $=cos(12.360^o+135^o)-cos(2.360^o+225^o)+tan(5.180^o+135^o)+cot(8.180^o+60^o)
=cos(90^o+45^o)-cos(180^o+45^o)+tan(90^o+45^o)+cot60^o$
$=-sin45^o+cos45^o-tan45^o+cot60^o=-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}-1+\frac{1}{3}=-\frac{2}{3}$.
b, Ta có $9^o và 81^o, 27^o và 63^o$ là các góc phụ nhau nên:
$tan81^o=tan(90^o-9^o)=-tan9^o$
$tan63^o=tan(90^o-27^o)=-tan27^o$
$\Rightarrow B=tan9^o-tan27^o+tan27^o-tan9^o=0$
c,ta có $2.sin^2a=1-cos2a$
$\Rightarrow 4.sin^4a=(1-cos2a)^2=1-2.cos2a+cos^22a=1-2.cos2a+\frac{1+cos4a}{2}$
$\Rightarrow 8.sin^4a=3-4cos2a+cos4a$ thay các giá trị $\frac{\Pi }{16},\frac{2\Pi }{16},...,\frac{15\Pi }{16}$ có
$8C=3.15+4(cos\frac{\Pi }{8}+cos\frac{2\Pi }{8}+...+cos\frac{15\Pi }{8})+3(cos\frac{\Pi }{4}+cos\frac{2\Pi }{4}+...+cos\frac{15\Pi }{4})$
$ =3.15-4-3=38$
$\Rightarrow C=\frac{38}{8}=\frac{19}{4}$.
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