tanα−tan(β−γ)1+tanαtan(β−γ)\frac{\tan\alpha-\tan\left(\beta-\gamma\right)}{1+\tan\alpha\tan\left(\beta-\gamma\right)}1+tanαtan(β−γ)tanα−tan(β−γ) sama dengan ....
tan(α−β+γ)\tan\left(\alpha-\beta+\gamma\right)tan(α−β+γ)
tan(α−β−γ)\tan\left(\alpha-\beta-\gamma\right)tan(α−β−γ)
tan(α+β+γ)\tan\left(\alpha+\beta+\gamma\right)tan(α+β+γ)
tan(α+β−γ)\tan\left(\alpha+\beta-\gamma\right)tan(α+β−γ)
tan(β+γ−α)\tan\left(\beta+\gamma-\alpha\right)tan(β+γ−α)
Rumus umum tangen dari selisih dua sudut adalah
tan(α−β)=tanα−tanβ1+tanαtanβ\tan\left(\alpha-\beta\right)=\frac{\tan\alpha-\tan\beta}{1+\tan\alpha\tan\beta}tan(α−β)=1+tanαtanβtanα−tanβ
Karena diketahui tanα−tan(β−γ)1+tanαtan(β−γ)\frac{\tan\alpha-\tan\left(\beta-\gamma\right)}{1+\tan\alpha\tan\left(\beta-\gamma\right)}1+tanαtan(β−γ)tanα−tan(β−γ) maka
tanα−tan(β−γ)1+tanαtan(β−γ)=tan(α−(β−γ))\frac{\tan\alpha-\tan\left(\beta-\gamma\right)}{1+\tan\alpha\tan\left(\beta-\gamma\right)}=\tan\left(\alpha-\left(\beta-\gamma\right)\right)1+tanαtan(β−γ)tanα−tan(β−γ)=tan(α−(β−γ))
=tan(α−β+γ)=\tan\left(\alpha-\beta+\gamma\right)=tan(α−β+γ)