c)

\(\sqrt{\left(\sqrt{2}-3\right)^2}-\sqrt{3+2\sqrt{2}}\\ =\left|\sqrt{2}-3\right|-\sqrt{2+2\sqrt{2}+1}\)

\(=3-\sqrt{2}-\sqrt{\left(\sqrt{2}+1\right)^2}\) (\(\sqrt{2}-3< 0\))

\(=3-\sqrt{2}-\left|\sqrt{2}+1\right|\)

\(=3-\sqrt{2}-\left(\sqrt{2}+1\right)\) (vì \(\sqrt{2}+1>0\))

\(=3-\sqrt{2}-\sqrt{2}-1\\ =2-2\sqrt{2}\)

`1/2+1/2+1/3+1/3`

`=(1/2+1/2)+(1/3+1/3)`

`=2/2+2/3`

`=1+2/3`

`=3/3+2/3`

`=5/3`

`x+1/2 xx x =4/5`

`x xx (1+1/2)=4/5`

`x xx (2/2+1/2)=4/5`

`x xx 3/2=4/5`

`x=4/5:3/2`

`x=4/5xx2/3`

`x=8/15`

\(\sqrt{6+2\sqrt{5-\sqrt{13+4\sqrt{3}}}}\\ =\sqrt{6+2\sqrt{5-\sqrt{12+2\cdot2\sqrt{3}+1}}}\\ =\sqrt{6+2\sqrt{5-\sqrt{\left(\sqrt{12}+1\right)^2}}}\)

\(=\sqrt{6+2\sqrt{5-\left|2\sqrt{3}+1\right|}}\)

\(=\sqrt{6+2\sqrt{5-\left(2\sqrt{3}+1\right)}}\) (vì \(2\sqrt{3}+1>0\))

\(=\sqrt{6+2\sqrt{5-2\sqrt{3}-1}}\\ =\sqrt{6+2\sqrt{4-2\sqrt{3}}}\\ =\sqrt{6+2\sqrt{3-2\cdot\sqrt{3}+1}}\\ =\sqrt{6+2\sqrt{\left(\sqrt{3}-1\right)^2}}\) 

\(=\sqrt{6+2\cdot\left|\sqrt{3}-1\right|}\) 

\(=\sqrt{6+2\cdot\left(\sqrt{3}-1\right)}\) (vì \(\sqrt{3}-1>0\))

\(=\sqrt{6+2\sqrt{3}-2}\\ =\sqrt{4+2\sqrt{3}}\\ =\sqrt{3+2\cdot\sqrt{3}+1}\\ =\sqrt{\left(\sqrt{3}+1\right)^2}\\ =\left|\sqrt{3}+1\right|\)

\(=\sqrt{3}+1\) (vì \(\sqrt{3}+1>0\))

\(=\sqrt{10+2\sqrt{17-4\sqrt{5+4\sqrt{5}+4}}}\)

\(=\sqrt{10+2\sqrt{17-4\sqrt{\left(\sqrt{5}+2\right)^2}}}\)

\(=\sqrt{10+2\sqrt{17-4\cdot\left|\sqrt{5}+2\right|}}\)

\(=\sqrt{10+2\sqrt{17-4\left(\sqrt{5}+2\right)}}\) (vì \(\sqrt{5}+2>0\))

\(=\sqrt{10+2\sqrt{17-4\sqrt{5}-8}}\)

\(=\sqrt{10+2\sqrt{9-4\sqrt{5}}}\\ =\sqrt{10+2\sqrt{5-4\sqrt{5}+4}}\\ =\sqrt{10+2\sqrt{\left(\sqrt{5}-2\right)^2}}\\ =\sqrt{10+2\cdot\left|\sqrt{5}-2\right|}\)

\(=\sqrt{10+2\cdot\left(\sqrt{5}-2\right)}\) (vì \(\sqrt{5}-2>0\))

\(=\sqrt{10+2\sqrt{5}-4}\\ =\sqrt{6+2\sqrt{5}}\\ =\sqrt{5+2\sqrt{5}+1}\\ =\sqrt{\left(\sqrt{5}+1\right)^2}\\ =\left|\sqrt{5}+1\right|\)

\(=\sqrt{5}+1\) (vì \(\sqrt{5}+1>0\))

`3x-15/(5*8)-15/(8*11)-15/(11*14)-...-15/(47*50)=2 1/10`

`3x-(15/(5*8)+15/(8*11)+15/(11*14)+...+15/(47*50))=21/10`

`3x-5(3/(5*8)+3/(8*11)+3/(11*14)+...+3/(47*50))=21/10`

`3x-5(1/5-1/8+1/8-1/11+1/11-1/14+...+1/47-1/50)=21/10`

`3x-5(1/5-1/50)=21/10`

`3x-5*9/50=21/10`

`3x-9/10=21/10`

`3x=21/10+9/10`

`3x=3`

`x=1`

có `cos α=1/2`

`=>cos^2 α=1/4`

Mà `cos^2 α +sin^2 α=1`

`=>1/4+sin^2 α=1`

`=>sin^2 α=1-1/4=3/4`

\(=>sin\alpha=\dfrac{\sqrt{3}}{2}\) (vì `sin α` >0)

ta có `sin α : cos α=tan α`

\(=>tan\alpha=\dfrac{\sqrt{3}}{2}:\dfrac{1}{2}=\sqrt{3}\)

ta có `tan α * cot α =1`

\(=>\sqrt{3}\cdot cot\alpha=1\\ =>cot\alpha=\dfrac{1}{\sqrt{3}}\)

tương tự ta có

\(\left\{{}\begin{matrix}sin\beta=\dfrac{\sqrt{2}}{2}\\cos\beta=1\\cot\beta=1\end{matrix}\right.\)