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Trigonometric Identities — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTrigonometric Identities1 Mark
MCQ
$\frac{\cos ^2 \theta}{\sin ^2 \theta}-\frac{1}{\sin ^2 \theta}$, in simplified form, is
  • A
    $\tan ^2 \theta$
  • B
    $\sec ^2 \theta$
  • C
    1
  • ✓
    -1
✓

Answer

Correct option: D.
-1
(D)-1
$\frac{\cos ^2 \theta}{\sin ^2 \theta}-\frac{1}{\sin ^2 \theta}$
$=\left(\frac{\cos \theta}{\sin \theta}\right)^2-\left(\frac{1}{\sin \theta}\right)^2$
$=\cot ^2 \theta-\operatorname{cosec}^2 \theta$
$=-\left(\operatorname{cosec}^2 \theta-\cot ^2 \theta\right)=-1$

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