A line makes angles $\propto, \beta, \gamma$ with the co-ordinate axes, then $\cos 2 \propto+\cos 2…

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
  1. 2
  2. $-1$
  3. 1
  4. $-2$

Solution

$\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma$ $=2 \cos ^{2} \alpha-1+2 \cos ^{2} \beta-1+2 \cos ^{2} \gamma-1$ $=2\left(\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma\right)-3=2(1)-3=-1$

Asked in: MHT CET 2020 (15 Oct Shift 2)

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