![image](https://tex.z-dn.net/?f=a%29+%5C+%5Cfrac%7B8sina-9cosa%7D%7B6cosa-7sina%7D%5C+%3D%2A%5C%5C%0Atga%3D2%3D%3E%5C+%5Cfrac%7Bsina%7D%7Bcosa%7D%3D2%5C+%3D%3E%5C+sina%3D2cosa%5C%5C%0A%2A%3D%5Cfrac%7B8%2A2cosa-9cosa%7D%7B6cosa-7%2A2cosa%7D%3D%5Cfrac%7B7cosa%7D%7B-8cosa%7D%3D-%5Cfrac%7B7%7D%7B8%7D%5C%5C%0Ab%29%5C+%5Cfrac%7Bsina%2B2cosa%7D%7B4cosa-3sina%7D%3D5%5C%5C%0A4cosa-3sina+%5Cneq+0%5C+%3D%3E%5C+3sina%5Cneq+4cosa%5C+%3D%3E%5Cfrac%7Bsina%7D%7Bcosa%7D%5Cneq+%5Cfrac%7B4%7D%7B3%7D%5C+%3D%3E+%5C%5C%0A%3D%3E%5C+tga+%5Cneq+%5Cfrac%7B4%7D%7B3%7D%5C%5C%0Asina%2B2cosa%3D5%2A%284cosa-3sina%29%5C%5C%0Asina%2B2cosa%3D20cosa-15sina%5C%5C%0A16sina%3D18cosa%5C%5C%0A%5Cfrac%7Bsina%7D%7Bcosa%7D%3D%5Cfrac%7B18%7D%7B16%7D%5C%5C%0Atga%3D1%5Cfrac%7B1%7D%7B8%7D)
\ \frac{sina}{cosa}=2\ =>\ sina=2cosa\\
*=\frac{8*2cosa-9cosa}{6cosa-7*2cosa}=\frac{7cosa}{-8cosa}=-\frac{7}{8}\\
b)\ \frac{sina+2cosa}{4cosa-3sina}=5\\
4cosa-3sina \neq 0\ =>\ 3sina\neq 4cosa\ =>\frac{sina}{cosa}\neq \frac{4}{3}\ => \\
=>\ tga \neq \frac{4}{3}\\
sina+2cosa=5*(4cosa-3sina)\\
sina+2cosa=20cosa-15sina\\
16sina=18cosa\\
\frac{sina}{cosa}=\frac{18}{16}\\
tga=1\frac{1}{8}" alt="a) \ \frac{8sina-9cosa}{6cosa-7sina}\ =*\\
tga=2=>\ \frac{sina}{cosa}=2\ =>\ sina=2cosa\\
*=\frac{8*2cosa-9cosa}{6cosa-7*2cosa}=\frac{7cosa}{-8cosa}=-\frac{7}{8}\\
b)\ \frac{sina+2cosa}{4cosa-3sina}=5\\
4cosa-3sina \neq 0\ =>\ 3sina\neq 4cosa\ =>\frac{sina}{cosa}\neq \frac{4}{3}\ => \\
=>\ tga \neq \frac{4}{3}\\
sina+2cosa=5*(4cosa-3sina)\\
sina+2cosa=20cosa-15sina\\
16sina=18cosa\\
\frac{sina}{cosa}=\frac{18}{16}\\
tga=1\frac{1}{8}" align="absmiddle" class="latex-formula">