Question

Найдите соѕ А, если tg A = 0,5.​

Answer 1

$\frac{2\sqrt{5}}{5}$

Объяснение:

$tgA=\frac{sinA}{cosA}=\frac{\sqrt{1-cos^{2}A}}{cosA};$

$tgA=0,5=\frac{1}{2}, \quad tgA=\frac{\sqrt{1-cos^{2}A}}{cosA} \Rightarrow \frac{\sqrt{1-cos^{2}A}}{cosA}=\frac{1}{2} \Rightarrow \frac{1-cos^{2}A}{cos^{2}A}=\frac{1}{4} \Rightarrow$

$\Rightarrow \frac{1}{cos^{2}A}-1=\frac{1}{4} \Rightarrow \frac{1}{cos^{2}A}=1+\frac{1}{4} \Rightarrow \frac{1}{cos^{2}A}=\frac{5}{4} \Rightarrow cos^{2}A=\frac{4}{5} \Rightarrow cosA=\sqrt{\frac{4}{5}} \Rightarrow$

$\Rightarrow cosA=\frac{\sqrt{4}}{\sqrt{5}} \Rightarrow cosA=\frac{2}{\sqrt{5}}=\frac{2\sqrt{5}}{5};$