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Trigonometric Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Functions1 Mark
MCQ
Choose the correct answer. The value of $\tan3\text{A}-\tan2\text{A}-\tan\text{A}$ is equal to:
  • ✓
    $\tan3\text{A}\tan2\text{A}\tan\text{A}$
  • B
    $-\tan3\text{A}\tan2\text{A}\tan\text{A}$
  • C
    $\tan\text{A}\tan2\text{A}-\tan2\text{A}\tan3\text{A}\tan\text{A}$
  • D
    $\text{None of these}$
✓

Answer

Correct option: A.
$\tan3\text{A}\tan2\text{A}\tan\text{A}$
$3\text{A}=\text{A}+2\text{A}$
$\Rightarrow\tan3\text{A}=\tan(\text{A+2A})$
$\Rightarrow\tan3\text{A}=\tan\text{A}+\tan\frac{2\text{A}}{1}-\tan\text{A}.\tan2\text{A}$
$\Rightarrow\tan\text{A}+\tan2\text{A}=\tan3\text{A}-\tan3\text{A}.\tan2\text{A}.\tan\text{A}$
$\Rightarrow\tan3\text{A}-\tan2\text{A}-\tan\text{A}=\tan3\text{A}.\tan2\text{A}.\tan\text{A}$

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