Question

If a line makes an angle α, β and γ with positive direction of the coordinate axes, then the value of sin²α + sin²β + sin²γ will be ______.

Options

• 1

• 3

• –2

• 2

Answer 1

If a line makes an angle α, β and γ with positive direction of the coordinate axes, then the value of sin²α + sin²β + sin²γ will be 2.

Explanation:

cos²α + cos²β + cos²γ = 1

`\implies` 1 – sin²α + 1 – sin²β + 1 – sin²γ = 1

`\implies` 3 – (sin²α + sin²β + sin²γ) = 1

`\implies` sin²α + sin²β + sin²γ = 2