MCQ
$\left(1+\tan ^2 \theta\right) \cos ^2 \theta=$ ?
- A$0$
- B$2$
- C$3$
- ✓$1$
✓
Answer
Correct option: D.
$1$
$\left(1+\tan ^2 \theta\right) \cos ^2 \theta$
$=\sec ^2 \theta \cdot \cos ^2 \theta\left[\because 1+\tan ^2 \theta=\sec ^2 \theta\right]$
$=\sec ^2 \theta \times \frac{1}{\sec ^2 \theta}=1 \left[\cos \theta=\frac{1}{\sec \theta}\right]$
$=\sec ^2 \theta \cdot \cos ^2 \theta\left[\because 1+\tan ^2 \theta=\sec ^2 \theta\right]$
$=\sec ^2 \theta \times \frac{1}{\sec ^2 \theta}=1 \left[\cos \theta=\frac{1}{\sec \theta}\right]$
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