Question

A line makes the same angle θ with each of the X and Z-axes. If the angle β, which it makes with Y-axis, is such that sin²β=3sin²θ, then cos²θ equals

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

Hint:

Use direction cosine identity l²+m²+n²=1.

Answer 1

The Correct Option is C

Let direction cosines be l=n=cosθ, m=cosβ. l²+m²+n²=1 ⟹ 2cos²θ+cos²β=1 sin²β=1-cos²β=3(1-cos²θ) Solving gives cos²θ=(3)/(5).