MHT CET · Maths · Three Dimensional Geometry
A line makes angles \(\propto, \beta, \gamma\) with the co-ordinate axes, then \(\cos 2 \propto+\cos 2 \beta+\cos 2 \gamma\)
is equal to
- A 2
- B \(-1\)
- C 1
- D \(-2\)
Answer & Solution
Correct Answer
(B) \(-1\)
Step-by-step Solution
Detailed explanation
\(\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma\)
\(=2 \cos ^{2} \alpha-1+2 \cos ^{2} \beta-1+2 \cos ^{2} \gamma-1\)
\(=2\left(\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma\right)-3=2(1)-3=-1\)
\(=2 \cos ^{2} \alpha-1+2 \cos ^{2} \beta-1+2 \cos ^{2} \gamma-1\)
\(=2\left(\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma\right)-3=2(1)-3=-1\)
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