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![](https://rs.olm.vn/images/avt/0.png?1311)
sin a=3/5
=>cos a=4/5
tan a=3/5:4/5=3/4; cot a=1:3/4=4/3
M=(4/3+3/4):(4/3-3/4)=25/7
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(\tan\alpha-\cot\alpha\right)^2-\left(\tan\alpha+\cot\alpha\right)^2\)
\(=\left(\tan\alpha-\cot\alpha+\tan\alpha+\cot\alpha\right)\)\(\left(\tan\alpha-\cot\alpha-\tan\alpha-\cot\alpha\right)\)
\(=\left(2.\tan\alpha\right).\left(-2.\cot\alpha\right)\)
\(=\left(-4\right).\tan\alpha.\cot\alpha\)
\(=-4\)
![](https://rs.olm.vn/images/avt/0.png?1311)
cộng hai vế ta được: 2tan\(\alpha\)=\(\frac{31}{12}\)\(\Rightarrow\)tan\(\alpha\)=\(\frac{31}{24}\)
=> cot\(\alpha\)=\(\frac{17}{24}\)
mik nham r . hai cau nay rieng biet nha , ko lien quan j toi nhau
![](https://rs.olm.vn/images/avt/0.png?1311)
\(cos^2\alpha=1-sin^2\alpha=1-\left(0,8\right)^2=0,36\)
\(\Rightarrow cos\alpha=0,6\)
\(1+cot^2\alpha=\dfrac{1}{sin^2\alpha}\Rightarrow cot^2\alpha=\dfrac{1}{sin^2\alpha}-1=\dfrac{9}{16}\)
\(\Rightarrow cot\alpha=0,75\)
\(tan\alpha=\dfrac{1}{cot\alpha}=\dfrac{1}{0,75}=\dfrac{4}{3}\)
\(\tan\alpha+\cot\alpha=2\Leftrightarrow\tan\alpha+\frac{1}{\tan\alpha}=2\)
\(\Rightarrow\tan^2\alpha+1=2\tan\alpha\)
\(\Leftrightarrow\tan\alpha=1\Rightarrow\alpha=45\)