sin20<sin70

cos25 > cos65*15'

tan73*20' >tan45

cotg2 >cotg73*40'

tan25>sin25

cotg32 >cos32

cot a=1/5 nên cosa/sina=1/5

=>sina=5cosa

\(1+cot^2a=\dfrac{1}{sin^2a}=1+\dfrac{1}{25}=\dfrac{26}{25}\)

nên \(sina=\dfrac{5}{\sqrt{26}}\Leftrightarrow cosa=\dfrac{1}{\sqrt{26}}\)

\(cot^4a+sin^2a-cos^2a\)

\(=\dfrac{1}{5^4}+25cos^2a-cos^2a\)

\(=\dfrac{1}{5^4}+24\cdot\dfrac{1}{26}=\dfrac{7513}{8125}\)

Chọn A

a/ \(\sin\alpha=\frac{C_đ}{C_h}\)

\(\cos\alpha=\frac{C_k}{C_h}\)

\(\Rightarrow\frac{\sin\alpha}{\cos\alpha}=\frac{\frac{C_đ}{C_h}}{\frac{C_k}{C_h}}=\frac{C_đ}{C_k}=\tan\alpha\)

b/ \(\frac{\cos\alpha}{\sin\alpha}=\frac{\frac{C_k}{C_h}}{\frac{C_đ}{C_h}}=\frac{C_k}{C_đ}=\cot\alpha\)

c/ \(\tan\alpha.\cot\alpha=\frac{C_đ}{C_k}.\frac{C_k}{C_đ}=1\)

d/ \(\sin^2\alpha=\frac{C_đ^2}{C_h^2}\)

\(\cos^2\alpha=\frac{C_k^2}{C_h^2}\)

\(\Rightarrow\sin^2\alpha+\cos^2\alpha=\frac{C_đ^2+C_k^2}{C_h^2}=\frac{C_h^2}{C_h^2}=1\)

P/s: hok trc lp 9 hay sao mà lm bài bài này?

uk. mk học trc lp 9

\(\sin60^o=\cos30^o\)

\(\cos75^o=\sin15^o\)

\(\cot82^o=\tan8^o\)

\(\tan80^o=\cot10^o\)

\(\sin52^o3'=\cos37^o57'\)

\(sin60=cos\left(90^0-60^0\right)=cos30^0\)

\(cos75^0=sin\left(90^0-75^0\right)=sin15^0\)

\(cot82^0=tan\left(90^0-82^0\right)=tan8^0\)

\(tan80^0=cot\left(90^0-80^0\right)=cot10^0\)

\(sin52^03'=cos\left(90^0-52^03'\right)=cos37^057'\)

Chọn D

Bài 2: 

\(\cos a=\sqrt{1-\left(\dfrac{7}{25}\right)^2}=\dfrac{24}{25}\)

\(\tan a=\dfrac{7}{25}:\dfrac{24}{25}=\dfrac{7}{24}\)

\(\cot a=\dfrac{24}{7}\)