Question

tan(4t)-tan(7t)=1+tan(7t)tan(4t)

Answer 1

\(\large\tt \begin{align} \color{black}{tan(4t)-tan(7t)=1+tan(7t)tan(4t)\\~\\
\dfrac{tan(4t)-tan(7t)}{1+tan(7t)tan(4t)}=1\\~\\
\color{blue}{[tan(a)-tan(b)=\dfrac{tana-tanb}{1+tana+tanb}]}\\~\\
tan(4t-7t)=1\\~\\
tan(-3t)=tan(\dfrac{\pi}{4})\\~\\
tan(2\pi-3t)=tan(\dfrac{\pi}{4})\\~\\
2\pi-3t=\dfrac{\pi}{4}\\~\\
t=\dfrac{7\pi}{12}\\~\\
}\end{align}\)