Consider the following relations among the anglesα, β and γ made by a vector with the coordinate axes$I.\cos 2\alpha +\cos 2\beta +\cos 2\gamma =-1$II. sin2α+sin2β+sin2γ=1$Whichoftheabovei\frac{s}{a}rec\text{or}rect?$

[a] We have. cos2α+cos2β+cos2γ=1          ??(i) ⇒2cos2α+2cos2β+2cos2γ=2 ⇒2cos2α−1+2cos2β−1+2cos2γ−1=2−3 ⇒cos2α+cos2β+cos2γ=−1 Hence statement- I is correct. And now from (i), 1−sin2α+1−sin2β+1−sin2γ=1 ⇒sin2α+sin2β+sin2γ=2 Hence, only statement I is correct.