CUET · MATHS · PYQ PAPER 2025
If a line makes angles \(\alpha, \beta, \gamma\) with the positive directions of \(x\)-axis, \(y\)-axis, \(z\)-axis respectively, then the value of \(\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma\) is equal to:
- A 1
- B -1
- C \(\frac{1}{2}\)
- D \(-\frac{1}{2}\)
Answer & Solution
Correct Answer
(B) -1
Step-by-step Solution
Detailed explanation
\(\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1\) \(\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma = (2\cos^2 \alpha - 1) + (2\cos^2 \beta - 1) + (2\cos^2 \gamma - 1)\) \(= 2(\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma) - 3\) \(= 2(1) - 3 = -1\)
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