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A line makes equal angles α, β and γ with the positive directions of the coordinate axes. If θ satisfies cos θ = (cos²α + cos²β + cos²γ) / (sin²α + sin²β + sin²γ), then what is the value of θ?
- π/3
- π/6
- π/2
- π/4
Correct answer: π/3
Solution
The equation given relates the cosines and sines of angles α, β, and γ, which are equal due to the line making equal angles with the axes. By substituting the equal angles into the equation, it simplifies to show that cos θ equals 1/2, which corresponds to θ being π/3.
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