MCQ
$\left(1-\sin ^2 \theta\right) \sec ^2 \theta=$ ?
- A$0$
- ✓1
- C2
- D3
✓
Answer
Correct option: B.
1
(b)
$\begin{aligned} & \left(1-\sin ^2 \theta\right) \sec ^2 \theta \\ = & \cos ^2 \theta \cdot \sec ^2 \theta\left[\because 1-\sin ^2 \theta=\cos ^2 \theta\right] \\ = & \cos ^2 \theta \times \frac{1}{\cos ^2 \theta}\left[\because \sec \theta=\frac{1}{\cos \theta}\right] \\ = & 1\end{aligned}$
$\begin{aligned} & \left(1-\sin ^2 \theta\right) \sec ^2 \theta \\ = & \cos ^2 \theta \cdot \sec ^2 \theta\left[\because 1-\sin ^2 \theta=\cos ^2 \theta\right] \\ = & \cos ^2 \theta \times \frac{1}{\cos ^2 \theta}\left[\because \sec \theta=\frac{1}{\cos \theta}\right] \\ = & 1\end{aligned}$
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