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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
If $A + B + C =180^{\circ}$, then $\tan A +\tan B +\tan C$ is equal to
  • ✓
    $\tan A \tan B \tan C$
  • B
    $2 \tan A \tan B \tan C$
  • C
    $-\tan A \tan B \tan C$
  • D
    $1-4 \tan A \tan B \tan C$
✓

Answer

Correct option: A.
$\tan A \tan B \tan C$
(A)
$\tan ( A + B )=\tan \left(180^{\circ}- C \right)$
$\Rightarrow \frac{\tan A+\tan B}{1-\tan A \tan B}=-\tan C$
$\Rightarrow \tan A+\tan B=-\tan C(1-\tan A \tan B)$
$\Rightarrow \tan A+\tan B=-\tan C+\tan A \tan B \tan C$
$\Rightarrow \tan A+\tan B+\tan C=\tan A \tan B \tan C$

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