a/ \(A=\frac{cot^2a-cos^2a}{cot^2a}-\frac{sina.cosa}{cota}\)

\(=\frac{\frac{cos^2a}{sin^2a}-cos^2a}{\frac{cos^2a}{sin^2a}}-\frac{sina.cosa}{\frac{cosa}{sina}}\)

\(=\left(1-sin^2a\right)-sin^2a=1\)

b/ \(B=\left(cosa-sina\right)^2+\left(cosa+sina\right)^2+cos^4a-sin^4a-2cos^2a\)

\(=cos^2a-2cosa.sina+sin^2a+cos^2a+2cosa.sina+sin^2a+\left(cos^2a+sin^2a\right)\left(cos^2a-sin^2a\right)-2cos^2a\)

\(=2+\left(cos^2a-sin^2a\right)-2cos^2a\)

\(=2-sin^2a-cos^2a=2-1=1\)

Ta có:

\(\hept{\begin{cases}cosa-sina=\frac{1}{5}\\sin^2a+cos^2a=1\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}cosa=\frac{1}{5}+sina\left(1\right)\\sin^2a+\left(\frac{1}{5}+sina\right)^2=1\left(2\right)\end{cases}}\)

\(\Rightarrow\left(2\right)\Leftrightarrow25sin^2a+5sina-12=0\)

\(\Leftrightarrow\orbr{\begin{cases}sina=-\frac{4}{5}\left(l\right)\\sina=\frac{3}{5}\end{cases}}\)

\(\Rightarrow cosa=\frac{4}{5}\)

\(\Rightarrow\hept{\begin{cases}tana=\frac{3}{4}\\cota=\frac{4}{3}\end{cases}}\)

Gấp gáp chi em cuộc sống vẫn rực rỡ sắc màu

Chim vẫn reo ca và môi hôn đang đứng đợi

Hoa vẫn nở và xuân thì đương tới

Hãy trải lòng xao xuyến với tình yêu.

a ) \(\tan\alpha=\dfrac{3}{4}\Rightarrow\alpha=36^052'11,63"\)

b ) \(\sin\alpha=0,5\Rightarrow\alpha=\dfrac{1}{2}\)

c ) \(\cos\alpha=\dfrac{2}{5}\Rightarrow\alpha=66^025'18,56"\)

d ) \(\cot\alpha=3\Rightarrow\alpha=18^026'5,82"\)

câu b bác lm sai rùi

a.Ta có \(\tan\alpha.\cot\alpha=1\Rightarrow\tan\alpha=\frac{1}{\cot\alpha}\)

\(\Rightarrow\frac{1}{\cot\alpha}+\cot\alpha=2\Rightarrow\cot^2\alpha-2\cot\alpha+1=0\)

\(\cot\alpha=1\Rightarrow\alpha=45^0\)

b.Ta có \(\sin^2\alpha+\cos^2\alpha=1\Rightarrow\cos^2\alpha=1-\sin^2\alpha\)

\(\Rightarrow7.\sin^2\alpha+5\left(1-\sin^2\alpha\right)=\frac{13}{2}\)\(\Leftrightarrow\sin^2\alpha=\frac{3}{4}\Leftrightarrow\orbr{\begin{cases}sin\alpha=\frac{\sqrt{3}}{2}\\sin\alpha=\frac{-\sqrt{3}}{2}\end{cases}}\)

\(\Rightarrow\alpha=60^0\)