Question

Distance between the points \((a\cos\theta,\,0)\) and \((0,\,a\sin\theta)\) is

• A. \(a\)
• B. \(2a\)
• C. \(3a\)
• D. \(4a\)

Hint:

Combine the Pythagorean identity \(\sin^2\theta+\cos^2\theta=1\) with the distance formula for quick simplification.

Answer 1

The Correct Option is A

Step 1: Use the distance formula.
\[ d=\sqrt{(a\cos\theta-0)^2+(0-a\sin\theta)^2} =\sqrt{a^2\cos^2\theta+a^2\sin^2\theta}. \]
Step 2: Apply identity.
\(\cos^2\theta+\sin^2\theta=1\Rightarrow d=\sqrt{a^2}=a\) (assuming \(a\ge 0\)).