b) Ta có: \(\sin^2\alpha+\cos^2\alpha=1\)

\(\Leftrightarrow\cos^2\alpha=\dfrac{16}{25}\)

hay \(\cos\alpha=\dfrac{4}{5}\)

Ta có: \(A=5\cdot\sin^2\alpha+6\cdot\cos^2\alpha\)

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

\(=5\cdot\dfrac{9}{25}+6\cdot\dfrac{16}{25}\)

\(=\dfrac{141}{25}\)

c) Ta có: \(\tan\alpha=\dfrac{1}{\cot\alpha}=\dfrac{1}{\dfrac{4}{3}}=\dfrac{3}{4}\)

\(D=\dfrac{\sin\alpha+\cos\alpha}{\sin\alpha-\cos\alpha}\)

\(=\dfrac{\dfrac{9}{16}+\dfrac{16}{9}}{\dfrac{9}{16}-\dfrac{16}{9}}=-\dfrac{337}{175}\)

1: 

a: sin a=căn 3/2

\(cosa=\sqrt{1-sin^2a}=\sqrt{1-\dfrac{3}{4}}=\sqrt{\dfrac{1}{4}}=\dfrac{1}{2}\)

\(tana=\dfrac{\sqrt{3}}{2}:\dfrac{1}{2}=\sqrt{3}\)

cot a=1/tan a=1/căn 3

b: \(tana=2\)

=>cot a=1/tan a=1/2

\(1+tan^2a=\dfrac{1}{cos^2a}\)

=>\(\dfrac{1}{cos^2a}=5\)

=>cos^2a=1/5

=>cosa=1/căn 5

\(sina=\sqrt{1-cos^2a}=\sqrt{\dfrac{4}{5}}=\dfrac{2}{\sqrt{5}}\)

c: \(cosa=\sqrt{1-\left(\dfrac{5}{13}\right)^2}=\dfrac{12}{13}\)

tan a=5/13:12/13=5/12

cot a=1:5/12=12/5

a: \(cos70=sin20\)

20<25

=>\(sin20< sin25\)

=>\(cos70< sin25\)

b: \(\dfrac{sin50}{cos40}=\dfrac{cos\left(90-50\right)}{cos40}=\dfrac{cos40}{cos40}=1\)

a) Ta có: 

\(cos70^o=sin\left(90^o-70^o\right)=sin20^o\)

Ta so sánh \(sin25^o\) và \(sin20^o\)

\(25^o>20^o\Rightarrow sin25^o>sin20^o\)

\(\Rightarrow sin25^o>cos70^o\)

b) \(\dfrac{sin50^o}{cos40^o}\)

Ta có: 

\(cos40^o=sin\left(90^o-40^o\right)=sin50^o\)

\(\Rightarrow\dfrac{sin50^o}{cos40^o}=\dfrac{sin50^o}{sin50^o}=1\)

Ta có: \(A=\sin^25^0+\sin^225^0+\sin^245^0+\sin^265^0+\sin^285^0\)

\(=\left(\sin^25^0+\sin^285^0\right)+\left(\sin^225^0+\sin^265^0\right)+\dfrac{1}{2}\)

\(=2+\dfrac{1}{2}=\dfrac{5}{2}\)

\(\Rightarrow A=\left(sin^25^0+sin^285^0\right)+\left(sin^225^0+sin^265^0\right)+sin^245^0=\left(sin^25^0+cos^25^0\right)+\left(sin^225^0+cos^225^0\right)+\dfrac{1}{2}=1+1+\dfrac{1}{2}=\dfrac{5}{2}\)

sina=cos(90-a) thay vào ta được

sin²15+sin²25+sin²35+cos²35+cos²25+cos²15=3

tương tự câu dưới ta được =3/2

Với  0 ° < α < 90 °  ta có α tăng thì sin α tăng

Ta có:  25 °  <  75 ° , suy ra sin 25 °  < sin 75 °

a) \(\frac{1}{cos^2x}=1+tan^2x=1+\frac{9}{16}=\frac{25}{16}\)

\(\Leftrightarrow cos^2x=\frac{16}{25}\Leftrightarrow\orbr{\begin{cases}cosx=\frac{4}{5}\\cosx=\frac{-4}{5}\end{cases}}\)

- \(cosx=\frac{4}{5}\): 

\(sinx=cosxtanx=\frac{4}{5}.\frac{3}{4}=\frac{3}{5}\)

\(cotx=\frac{1}{tanx}=\frac{1}{\frac{3}{4}}=\frac{4}{3}\).

- \(cosx=\frac{-4}{5}\): 

\(sinx=cosxtanx=\frac{-4}{5}.\frac{3}{4}=\frac{-3}{5}\)

\(cotx=\frac{1}{tanx}=\frac{1}{\frac{3}{4}}=\frac{4}{3}\).

b)  \(sin^2x+cos^2x=1\Leftrightarrow cos^2x=1-sin^2x=1-\frac{49}{625}=\frac{576}{625}\)

\(\Leftrightarrow\orbr{\begin{cases}cosx=\frac{24}{25}\\cosx=-\frac{24}{25}\end{cases}}\)

- \(cosx=\frac{24}{25}\): 

\(tanx=\frac{sinx}{cosx}=\frac{\frac{7}{25}}{\frac{24}{25}}=\frac{7}{24}\)

\(tanx.cotx=1\Rightarrow cotx=\frac{1}{tanx}=\frac{1}{\frac{7}{24}}=\frac{24}{7}\)

- \(cosx=\frac{-24}{25}\): 

\(tanx=\frac{sinx}{cosx}=\frac{\frac{7}{25}}{\frac{-24}{25}}=-\frac{7}{24}\)

\(tanx.cotx=1\Rightarrow cotx=\frac{1}{tanx}=\frac{1}{-\frac{7}{24}}=\frac{-24}{7}\)