Question

Cho góc nhọn \(\alpha\) thỏa mãn \(0^o< \alpha< 70^o\) và biểu thức:
\(A=tan\alpha.tan\left(\alpha+10^o\right).tan\left(\alpha+20^o\right).tan\left(70^o-\alpha\right).tan\left(80^o-\alpha\right).tan\left(90^o-\alpha\right)\)
Giá trị của biểu thức \(A\) là:
A. 0                  B. 1                  C. 2                         D. 3

 

Answer 1

\(A=tan\alpha\cdot tan\left(\alpha+10^o\right)\cdot tan\left(\alpha+20^o\right)\cdot tan\left(70^o-\alpha\right)\cdot tan\left(80^o-\alpha\right)\cdot tan\left(90^o-\alpha\right)\)

\(A=tan\alpha\cdot tan\left(\alpha+10^o\right)\cdot tan\left(\alpha+20^o\right)\cdot tan\left(90^o-\left(\alpha+20^o\right)\right)\cdot tan\left(90^o-\left(\alpha+10^o\right)\right)\cdot tan\left(90^o-\alpha\right)\)

\(A=tan\alpha\cdot tan\left(\alpha+10^o\right)\cdot tan\left(\alpha+20^o\right)\cdot cot\left(\alpha+20\right)\cdot cot\left(\alpha+10^o\right)\cdot cot\alpha\)

Vì \(0^o< \alpha< 70^o\rightarrow10^o< \alpha+10^o< 80^o;20^o< \alpha+20^o< 90^o\)

\(\Rightarrow A=1\cdot1\cdot1=1\)

Chọn B