Bài 2:

$cos\alpha=\frac{1}{2}$

$\Rightarrow \alpha=60^o$

$sin\alpha=sin60^o=\frac{\sqrt{3}}{2}$

$tan\alpha=tan60^o=\sqrt{3}$

$cot\alpha=\frac{cos\alpha}{sin\alpha}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{\sqrt{3}}{3}$

Bài 3:

a) A=$(sin^215^o+sin^275^o)+(sin^225^o+sin^265^o)+(sin^235^o+sin^255^o)+sin^245^o$

=$[sin^2(90^o-75^o)+sin^275^o]+[sin^2(90^o-65^o)+sin^265^o]+[sin^2(90^o-55^o)+sin^255^o]+sin^245^o$

biết $cos\alpha=sin(90^o-\alpha)

=$[cos^275^o+sin^275^o]+[cos^265^o+sin^265^o]+[cos^255^o-sin^255^o]+sin^245^o$

biết $cos\alpha+sin\alpha=1$

=$1+1+1+(\frac{\sqrt{2}}{2})^2$

=$3+\frac{1}{2}$

=$\frac{7}{2}$

b) B=$tan10^o.tan80^o-tan20^o.tan70^o$

=$tan(90^o-80^o).tan80^o-tan(90^o-70^o).tan70^o$

biết $cot\alpha=tan(90^o-\alpha)$

=$cot80^o.tan80^o-cot70^o.tan70^o$

Biết $tan\alpha.cot\alpha=1$

=1 - 1

=0