MCQ
$\tan ^2 \theta \sin ^2 \theta$ is equal to
- ✓$\tan ^2 \theta-\sin ^2 \theta$
- B$\tan ^2 \theta+\sin ^2 \theta$
- C$\frac{\tan ^2 \theta}{\sin ^2 \theta}$
- D$\sin ^2 \theta \cot ^2 \theta$
✓
Answer
Correct option: A.
$\tan ^2 \theta-\sin ^2 \theta$
$\tan ^2 \theta - \sin ^2 \theta$
$=\frac{\sin ^2 \theta \sin ^2 \theta}{\cos ^2 \theta}$
$=\sin ^2 \theta\left(\frac{1-\cos ^2 \theta}{\cos ^2 \theta}\right)$
$=\frac{\sin ^2 \theta}{\cos ^2 \theta}-\sin ^2 \theta$
$=\tan ^2 \theta-\sin ^2 \theta$
$=\frac{\sin ^2 \theta \sin ^2 \theta}{\cos ^2 \theta}$
$=\sin ^2 \theta\left(\frac{1-\cos ^2 \theta}{\cos ^2 \theta}\right)$
$=\frac{\sin ^2 \theta}{\cos ^2 \theta}-\sin ^2 \theta$
$=\tan ^2 \theta-\sin ^2 \theta$
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