Question

If a line makes angles α,β,γ with the coordinate axes, then the value of

cos 2α + cos 2β + cos 2γ is____
A. 3
B. -2
C. 2
D.-1

Answer 1

The value of cos 2α + cos 2β + cos 2γ is -1.

So, the correct answer is: D. -1

Step-by-step explanation:

The value of cos 2α + cos 2β + cos 2γ can be found using trigonometric identities. Since the line makes angles α, β, and γ with the coordinate axes, we can use the identities:

Substituting these identities into the expression gives:

cos 2α + cos 2β + cos 2γ = cos^2(π/2 - α) + cos^2(π/2 - β) + cos^2(π/2 - γ)

= sin^2 α + sin^2 β + sin^2 γ

Since sine squared is always positive, the sum sin^2 α + sin^2 β + sin^2 γ is always greater than or equal to zero, so the value of cos 2α + cos 2β + cos 2γ is D. -1.