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Introduction of Trigonometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
MCQ
$\frac{\cot\theta}{\cot \theta-\cot3 \theta}+\frac{\tan\theta}{\tan\theta-\tan3\theta}$ is equal to :
  • A
    $0$
  • ✓
    $1$
  • C
    $-1$
  • D
    $2$
✓

Answer

Correct option: B.
$1$
$=\frac{\cot\theta}{\cot\theta-\cot3\theta}+\frac{\tan\theta}{\tan\theta-\tan3\theta}$
$=\frac{\cot\theta\tan\theta-\cot\theta\tan3\theta+\cot\theta\tan\theta-\tan\theta\cot3\theta}{(\cot\theta-\cot3\theta)(\tan\theta-\tan3\theta)}$
$\{\tan\theta\cot\theta=1\}$
$\Rightarrow\ \frac{1-\cot\theta\tan3\theta+1-\tan\theta\cot3\theta}{\cot\theta\tan\theta-\cot\theta\tan3\theta-\tan\theta\cot3\theta+\cot3\theta\tan3\theta}$
$=\frac{2-\cot\theta\tan3\theta-\tan\theta\cot3\theta}{1-\cot\theta\tan3\theta-\tan\theta\cot3\theta+1}$
$=\frac{2-\cot\theta\tan3\theta-\tan\theta\cot3\theta}{2-\cot\theta\tan\theta-\tan\theta\cot3\theta}=1$

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