If a line makes angles α,β,γwith coordinate axes respectively, then the value of ∑cos2α∑cos2α+∑sin2α=

If α,β,γ are the angles made by a line with axes in the positive direction then cos2α+cos2β+cos2γ=1 and sin2α+sin2β+sin2γ=1And consider the expressioncos2α+cos2β+cos2γUse the trigonometry identity cos2α=2cos2α−1It implies that cos2α+cos2β+cos2γ=2cos2α+cos2β+cos2γ−3=−1         Therefore,  ∑cos2α∑cos2α+∑sin2α=−11+2=−13