MCQ
The distance between the points $\big(\sin\theta,\cos\theta\big)$ and $\big(\cos\theta-\sin\theta\big)$ is :
- ✓$\sqrt{2\text{ units}}$
- B$\sqrt{\sin\theta+\cos\theta}\text{ units}$
- C$2\sqrt{2\text{ units}}$
- D$\text{2 units}$
✓
Answer
Correct option: A.
$\sqrt{2\text{ units}}$
Distance between $\big(\sin\theta,\cos\theta\big)$ and $\big(\cos\theta-\sin\theta\big)$
$=\sqrt{\big(\cos\theta-\sin\theta\big)^2+\big(-\sin\theta-\cos\theta\big)^2}$
$=\sqrt{2\cos^2\theta+{2\sin^2\theta}}$
$=\sqrt{2(\cos^2\theta+{2\sin^2\theta})}$
$\because[\cos^2\theta+\sin\theta=1]$
$=\sqrt{\text{2 units }}$
$=\sqrt{\big(\cos\theta-\sin\theta\big)^2+\big(-\sin\theta-\cos\theta\big)^2}$
$=\sqrt{2\cos^2\theta+{2\sin^2\theta}}$
$=\sqrt{2(\cos^2\theta+{2\sin^2\theta})}$
$\because[\cos^2\theta+\sin\theta=1]$
$=\sqrt{\text{2 units }}$
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