Question

If $A+B+C=\pi ,n\in Z$, then $\tan nA+\tan nB+\tan nC$ is equal to

• A. $0$
• B. $1$
• C. $\tan nA.\tan nB.\tan nC$
• D. None of these

Answer 1

The correct option is C $\tan nA.\tan nB.\tan nC$

$A+B+C=\pi \Rightarrow nA+nB+nC=n\pi \Rightarrow \tan (nA+nB+nC)=\tan n\pi$

$\Rightarrow \frac{(\tan nA+\tan nB+\tan nC)-\tan nA.\tan nB.\tan nC}{1-\tan nA.\tan nB-\tan nB.\tan nC-\tan nA.\tan nC}=0\Rightarrow \tan nA+\tan nB+\tan nC=\tan nA.\tan nB.\tan nC$