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Arithmetic Progressions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsArithmetic Progressions3 Marks
MCQ
$\tan3\text{A}-\tan2\text{A}-\tan\text{A}$ is equal to:
  • ✓
    $\tan3\text{A}\tan2\text{A}\tan\text{A}$
  • B
    $-\tan3\text{A}-\tan2\text{A}\tan\text{A}$
  • C
    $\tan\text{A}\tan2\text{A}\tan2\text{A}\tan3\text{A}-\tan3\text{A}\tan\text{A}$
  • D
    Non of these
✓

Answer

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

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