Question

Tính giá trị biểu thức

a, \(\tan15^o.\tan25^o.\tan35^o....\tan75^o\)

b, Cho \(\cos\alpha=\frac{20}{29}.\)Tính \(\tan\alpha,\cot\alpha,\sin\alpha\)

Answer 1

\(tan75^0=cot\left(90^0-75^0\right)=cot15^0\) tương tự ta có:

\(tan15.tan25.tan35...tan75=tan15.tan75.tan25.tan65.tan35.tan55.tan45\)

\(=tan15.cot15.tan25.cot25.tan35.cot35.tan45\)

\(=1.1.1=1\)

b/ \(sina=\pm\sqrt{1-cos^2a}=\pm\frac{21}{29}\)

\(\Rightarrow tana=\frac{sina}{cosa}=\pm\frac{21}{20}\); \(cota=\frac{1}{tana}=\pm\frac{20}{21}\)