Question

cho cot x = 8/15 . tính tan x , sin x , cos x

giúp em nha mng

Answer 1

Ta có: \(\tan x\cdot\cot x=1\Leftrightarrow\tan x\cdot\frac{8}{15}=1\Leftrightarrow\tan x=1:\frac{8}{15}=\frac{15}{8}\)

Lại có: \(\tan x=\frac{\sin x}{\cos x}=\frac{15}{8}\Leftrightarrow\sin x=\frac{15}{8}\cos x\)

Mặt khác:

\(\sin^2x+\cos^2x=1\\ \Leftrightarrow\left(\frac{15}{8}\cos x\right)^2+\cos^2x=1\\ \Leftrightarrow\frac{225}{64}\cos^2x+\cos^2x=1\\ \Leftrightarrow\frac{289}{64}\cos^2x=1\\ \Leftrightarrow\cos^2x=\frac{64}{289}\\ \Leftrightarrow\cos x=\frac{8}{17}\)

Suy ra: \(\sin x=\frac{15}{8}\cdot\cos x=\frac{15}{8}\cdot\frac{8}{17}=\frac{15}{17}\)