Question

A line makes the same angle \(\theta\) with each of the X and Z-axes. If the angle \(\beta\) which it makes with Y-axis is such that \(\sin^2\beta=3\sin^2\theta\), then \(\cos^2\theta\) equals

• A. \(2/5\)
• B. \(1/5\)
• C. \(3/5\)
• D. \(2/3\)

Hint:

Use \(l^2+m^2+n^2=1\).

Answer 1

The Correct Option is A

Step 1: Direction cosines: \[ l=m=\cos\theta \]
Step 2: \[ \sin^2\beta=1-m^2=3\sin^2\theta \]
Step 3: \[ 1-\cos^2\theta=3(1-\cos^2\theta) \Rightarrow \cos^2\theta=\frac25 \]