1,
ĐK: `sin (x/7) \ne 0 <=> x/7 \ne kπ <=> x \ne k7π`
Đặt `cot x/7 =t `, ta có PT:
`t^2-14t+13=0`
`<=>[(t=1),(t=13):}`
Với `t=1`:
`cot (x/7) =1 <=> x/7= π/4+kπ <=> x=(7π)/4+k7π (k in ZZ)`
Với `t=13`:
`cot (x/7) =13 <=> x/7 = arccot13+kπ <=> x=7.arccot13+k7π (k in ZZ)`
.
2,
`cot^2 (x/5)+3cot (x/5)+2=0`
`<=>` \(\left[ \begin{array}{l}cot \dfrac{x}{5}=-1\\cot \dfrac{x}{5}=-2\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}\dfrac{x}{5}=\dfrac{-π}{4}+kπ\\\dfrac{x}{5}=arccot(-2)+kπ\end{array} \right.\) \
`<=>`\(\left[ \begin{array}{l}x=\dfrac{-5π}{4}+k5π\\x=5 .arccot(-2)+k5π\end{array} \right.\)