Tan α = ?
[tex]\begin{aligned}\tan\alpha&=\boxed{\,\bf\frac{35}{12}\:=\:2\,\frac{11}{12}\:\approx\:2{,}91667\,}\end{aligned}[/tex]
Pembahasan
Sudut α, β, dan γ pada penyelesaian di bawah ini menurut gambar yang saya sertakan.
Dari gambar, dapat diamati bahwa α = 2(β – γ).
Maka:
[tex]\begin{aligned}\tan\alpha&=\tan\left[2(\beta-\gamma)\right]\\&=\frac{2\tan(\beta-\gamma)}{1-\tan^2(\beta-\gamma)}\\&\quad\left[\ \begin{aligned}\tan(\beta-\gamma)&=\frac{\tan\beta-\tan\gamma}{1+\tan\beta\tan\gamma}\\&=\frac{1\:-\:1/6}{1\:+\:1\cdot(1/6)}\\&=\frac{5/6}{7/6}\:=\:\frac{5}{7}\\\end{aligned}\right.\\&=\frac{2\cdot(5/7)}{1\:-\:(5/7)^2}\\&=\frac{10/7}{1\:-\:25/49}\\&=\frac{10/7}{24/49}=\frac{5/1}{12/7}=5\cdot\frac{7}{12}\end{aligned}[/tex]
[tex]\therefore\ \tan\alpha=\boxed{\,\bf\frac{35}{12}\:=\:2\,\frac{11}{12}\:\approx\:2{,}91667\,}[/tex]
[tex]\blacksquare[/tex]
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