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Question: If a line makes the angle \(\alpha , \beta , \gamma\) with three dimensional co-ordinate axes respec...

If a line makes the angle α,β,γ\alpha , \beta , \gamma with three dimensional co-ordinate axes respectively, then cos⁡2α+cos⁡2β+cos⁡2γ=\cos 2 \alpha + \cos 2 \beta + \cos 2 \gamma =

A

– 2

B

– 1

C

1

D

2

Answer

– 1

Explanation

Solution

cos⁡2α+cos⁡2β+cos⁡2γ\cos 2 \alpha + \cos 2 \beta + \cos 2 \gamma

=2cos⁡2α−1+2cos⁡2β−1+2cos⁡2γ−1= 2 \cos ^ { 2 } \alpha - 1 + 2 \cos ^ { 2 } \beta - 1 + 2 \cos ^ { 2 } \gamma - 1

=2(cos⁡2α+cos⁡2β+cos⁡2γ)−3=2−3=−1= 2 \left( \cos ^ { 2 } \alpha + \cos ^ { 2 } \beta + \cos ^ { 2 } \gamma \right) - 3 = 2 - 3 = - 1