Solveeit Logo
Login

Question

Mathematics Question on introduction to three dimensional geometry

If α ,β, γ \alpha \,,\beta,\,\gamma\, are the angles which a half ray makes with the positive directions of the axes, then sin⁡2α ,sin⁡2β, sin⁡2γ \sin^2\alpha \,,\sin^2\beta,\,\sin^2\gamma\, is equal to

A

1

B

2

C

0

D

-1

Answer

2

Explanation

Solution

cos⁡2 α+cos⁡2 β+cos⁡2 γ\cos^2 \, \alpha + \cos^2\, \beta + \cos^2\, \gamma = 1 ⇒\Rightarrow sin⁡2 α+sin⁡2 β+sin⁡2 γ\sin^2 \,\alpha + \sin^2 \, \beta + \sin^2\, \gamma = 2