If A + B = C, then write the value of .

Question

If A + B = C, then write the value of $\tan\text{A}\tan\text{B}\tan\text{C}.$

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Answer

We have, A + B = C
$\Rightarrow\tan(\text{A+B})=\tan\text{C}$
$\Rightarrow\frac{\tan\text{A}+\tan\text{B}}{1-\tan\text{A}\tan\text{B}}=\tan\text{C}$
$\Rightarrow\tan\text{A}+\tan\text{B}=\tan\text{C}-\tan\text{A}\tan\text{B}\tan\text{C}$
$\Rightarrow\tan\text{A}\tan\text{B}\tan\text{C}=\tan\text{C}-\tan\text{A}-\tan\text{B}$

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