\(c,cos^220^o+cos^250^o+cos^270^o+cos^240^o.\\ =cos^2\left(90^o-70^o\right)+cos^250^o+cos^270^o+cos^2\left(90^o-50^o\right).\\ =sin^270^o+cos^250^o+cos^270^o+sin^250^o.\\ =\left(sin^270^o+cos^270^o\right)+\left(cos^250^o+sin^250^o\right).\\ =1+1=2.\)

\(BT\Rightarrow\dfrac{\left(\sqrt{x}+2\right)^2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\dfrac{2}{\sqrt{x}-2}.\\ =\dfrac{\sqrt{x}+2}{\sqrt{x}-2}-\dfrac{2}{\sqrt{x}-2}.\\ =\dfrac{\sqrt{x}+2-2}{\sqrt{x}-2}=\dfrac{\sqrt{x}}{\sqrt{x}-2}.\)

\(\left(\dfrac{5}{2}-\dfrac{4}{3}\right).\dfrac{9}{14}=\dfrac{7}{6}.\dfrac{9}{14}=\dfrac{3}{4}.\\ \dfrac{5}{2}\left(\dfrac{2}{3}-\dfrac{1}{4}\right)=\dfrac{5}{2}.\dfrac{5}{12}=\dfrac{25}{24}.\\ \left(\dfrac{5}{2}+\dfrac{11}{8}\right).\left(\dfrac{8}{3}-\dfrac{20}{15}\right)=\left(\dfrac{5}{2}+\dfrac{11}{8}\right).\left(\dfrac{8}{3}-\dfrac{4}{3}\right)=\dfrac{31}{8}.\dfrac{4}{3}=\dfrac{31}{6}.\)

\(d,4\dfrac{1}{6}:2\dfrac{1}{3}=\dfrac{25}{6}:\dfrac{7}{3}=\dfrac{25}{6}.\dfrac{3}{7}=\dfrac{25}{14}.\)

Gọi giao điểm của OB và Ax là H.

Ta có: \(Ax//By\left(gt\right).\)

\(\rightarrow\widehat{OBy}+\widehat{AHO}=180^o\) (Do 2 góc ở vị trí trong cùng phía).

Mà \(\widehat{OBy}=122^o\left(gt\right).\)

\(\rightarrow\widehat{AHO}=180^o-122^o=58^o.\)

Xét \(\Delta AHO\) có:

\(\widehat{AHO}+\widehat{AOH}+\widehat{HAO}=180^o\) (Tổng 3 góc trong tam giác).

\(\Rightarrow58^o+\widehat{AOH}+32^o=180^o.\\ \Rightarrow\widehat{AOH}=180^o-58^o-32^o=90^o.\\ \Rightarrow OA\perp OB.\)

\(a,\left(a+b\right)^2\\ =\left(a+b\right)\left(a+b\right)\\ =a^2+ab+b^2+ab\\ =a^2+2ab+b^2.\)

\(b,\left(a-b\right)^2\\ =\left(a-b\right)\left(a-b\right)\\ =a^2-ab+b^2-ab\\ =a^2-2ab+b^2.\)

\(c,a^2-b^2\\ =a^2+ab-ab-b^2\\ =a\left(a+b\right)-b\left(a+b\right)\\ =\left(a-b\right)\left(a+b\right).\)

\(a)\sin36^o-\cos54^o.\\ =\sin\left(90^o-54^o\right)-\cos54^o.\\ =\cos54^o-\cos54^o=0.\)

\(b)\dfrac{\sin40^o}{\cos50^o}=\dfrac{\sin\left(90^o-50^o\right)}{\cos50^o}=\dfrac{\cos50^o}{\cos50^o}=1.\)

\(2)\\ A=\dfrac{1}{x-2}+\dfrac{1}{x+2}+\dfrac{x^2+1}{x^2-4}\left(x\ne2;-2\right).\\ A=\dfrac{x+2+x-2+x^2+1}{\left(x-2\right)\left(x+2\right)}.\\ A=\dfrac{x^2+2x+1}{\left(x-2\right)\left(x+2\right)}.\\ A=\dfrac{\left(x+1\right)^2}{x^2-4}.\)

\(4)\\ P=\left(\dfrac{1}{x}+\dfrac{x}{x+1}\right):\dfrac{x}{x^2+x}.\left(x\ne0;-1\right).\\ P=\dfrac{x+1+x^2}{x^2+x}:\dfrac{x}{x^2+x}.\\ P=\dfrac{x+1+x^2}{x^2+x}.\dfrac{x^2+x}{x}.\\ P=\dfrac{x^2+x+1}{x}.\)