\(\cot\alpha=\dfrac{1}{2}\)

\(\sin\alpha=\dfrac{kề}{\sqrt{5}kề}=\dfrac{\sqrt{5}}{5}\)

\(\cos\alpha=\sqrt{1-\dfrac{5}{25}}=\dfrac{2\sqrt{5}}{5}\)

MN K BT?

\(sin^2\alpha+cos^2\alpha=1\Rightarrow cos\alpha=\sqrt{1-sin^2\alpha}=\sqrt{1-\left(0,6\right)^2}=\frac{4}{5}\)

\(tan\alpha=\frac{sin\alpha}{cos\alpha}=\frac{0,6}{\frac{4}{5}}=\frac{3}{4}\)

\(cot\alpha=\frac{1}{tan\alpha}=\frac{1}{\frac{3}{4}}=\frac{4}{3}\)

Điều kiện: a>45 độ

\(sin^6a+cos^6a=\left(sin^2x\right)^3+\left(cos^2x\right)^3\)

\(=\left(sin^2x+cos^2x\right)\left(sin^4x+cos^4x-sin^2x.cos^2x\right)\)

\(=sin^4x+2sin^2xcos^2x+cos^4x-3sin^2x.cos^2x\)

\(=\left(sin^2x+cos^2x\right)^2-\frac{3}{4}.\left(2sinx.cosx\right)^2\)

\(=1-\frac{3}{4}sin^22x=1-\frac{3}{4}\left(\frac{1}{2}-\frac{1}{2}cos4x\right)=\frac{5}{8}+\frac{3}{8}cos4x\)

2/

\(\frac{1+sin2a-cos2a}{1+cos2a}=\frac{1+2sina.cosa-\left(1-2sin^2a\right)}{1+2cos^2a-1}=\frac{2sina.cosa+2sin^2a}{2cos^2a}\)

\(=\frac{2sina.cosa}{2cos^2a}+\frac{2sin^2a}{2cos^2a}=tana+tan^2a\)

1/ x thành α nha bạn

\(\tan\alpha+\cot\alpha=3\)

=>\(\frac{\sin\alpha}{cos\alpha}+\frac{cos\alpha}{\sin\alpha}=3\)

=>\(\frac{\sin^2\alpha+cos^2\alpha}{\sin\alpha\cdot cos\alpha}=3\)

=>\(\frac{1}{\sin\alpha\cdot cos\alpha}=3\)

=>\(\sin\alpha\cdot cos\alpha=\frac13\)

\(\tan^2\alpha+\cot^2\alpha=\left(\tan\alpha+\cot\alpha\right)^2-2\cdot tan\alpha\cdot\cot a\)

\(=3^2-2\)

=9-2

=7