Question
If A = B = 60°, verify that.
$\tan(\text{A}-\text{B})=\frac{\tan\text{A}-\tan\text{B}}{1-\tan\text{A}\tan\text{B}}$
$\tan(\text{A}-\text{B})=\frac{\tan\text{A}-\tan\text{B}}{1-\tan\text{A}\tan\text{B}}$
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Answer
$\Rightarrow\tan(\text{A}-\text{B})=\frac{\tan\text{A}-\tan\text{B}}{1-\tan\text{A}\tan\text{B}}$ put $\text{A}=\text{B}=60^\circ$ $\Rightarrow\tan(60^\circ-60^\circ)=\frac{\tan60^\circ-\tan60^\circ}{1-\tan60^\circ\tan60^\circ}$ $\tan0^\circ=\frac{0}{1-\tan^260^\circ}$$\Rightarrow0=0$
$\Rightarrow\text{L.H.S} = \text{R.H.S}$
$\Rightarrow\text{L.H.S} = \text{R.H.S}$
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