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Trigonometry — MATHS STD 10 — Question

Tamilnadu BoardEnglish MediumSTD 10MATHSTrigonometry1 Mark
MCQ
$\tan \theta \operatorname{cosec}^2 \theta-\tan \theta$ is equal to …………
  • A
    sec θ
  • B
    $cot^2$θ
  • C
    sin θ
  • ✓
    cot θ
✓

Answer

Correct option: D.
cot θ
$\cot \theta$
Explanation;
Hint:
$\tan \theta \operatorname{cosec}^2 \theta-\tan \theta=\tan \theta\left(\operatorname{cosec}^2 \theta-1\right)$
$=\tan \theta \times \cot ^2 \theta $
$=\frac{1}{\cot \theta} \times \cot ^2 \theta$
$=\cot \theta$

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