Question

If a straight line makes angles α, β and γ with the co-ordinate axes, then sin²α + sin²β + sin²γ is equal to

Answer 1

Correct Answer - Option 3 : 2

Concept Used:

If α, β, γ is the angle, a line makes with the co-ordinate axis,

Then, cos² α + cos² β + cos² γ = 1

cos² α = 1 – sin²α

Calculation:

cos² α + cos² β + cos² γ = 1

⇒ (1 − sin²α) + (1 − sin² β) + (1 − sin² γ) = 1

⇒ 3 − (sin²α + sin² β + sin² γ) = 1

∴ (sin²α + sin² β + sin² γ) = 2