\(cos^2b+sin^2b=1\\ \Leftrightarrow cos^2b=1-\left(\dfrac{3}{5}\right)^2=\dfrac{16}{25}\\ \Leftrightarrow cosb=\dfrac{4}{5}\left(0< b< \dfrac{\pi}{2}\right)\\tanb=\dfrac{sinb}{cosb}=\dfrac{\dfrac{3}{5}}{\dfrac{4}{5}}=\dfrac{3}{4}\)
\(tan\left(a+b\right)=\dfrac{tana+tanb}{1-tana.tanb}=\dfrac{\dfrac{1}{2}+\dfrac{3}{4}}{1-\dfrac{1}{2}.\left(\dfrac{3}{4}\right)}=2\)
\(tan\left(a-b\right)=\dfrac{tana-tanb}{1+tana.tanb}=-\dfrac{2}{11}\\ \Rightarrow cot\left(a-b\right)=\dfrac{1}{tan\left(a-b\right)}=-\dfrac{11}{2}\)
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