Prove that: 69^ + 66^ 1- 69^ 66^ =-1 - Vidyadip

Question

Prove that:$\frac{\tan69^\circ+\tan66^\circ}{1-\tan69^\circ\tan66^\circ}=-1$

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Answer

$\text{L.H.S}=\frac{\tan69^\circ+\tan66^\circ}{1-\tan69^\circ\tan66^\circ}$ $=\tan(69^\circ+66^\circ)$ $\Big[\because\tan\text{(A+B})=\frac{\tan\text{A}+\tan\text{B}}{1-\tan\text{A}\tan\text{B}}\Big]$ $=\tan(135^\circ)$ $=\tan(90^\circ+45^\circ)$$[\because\tan\theta$ is negetive in second quadrant$]$ $=-\cot45^\circ$ $=-1$ $=\text{R.H.S}$ $\therefore\text{L.H.S}=\text{R.H.S}$ Hence proved.

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