A line makes angles α,β,γ with coordinate axes. If β+γ=π2, then cosα+cosβ+cosγ2=

If α,β,γ are the angles made by a line ‘L’ with the coordinate axes in the positive direction then cos2α+cos2β+cos2γ=1Given α,β,γ=π2−βIt implies that cos2α+cos2β+sin2β=1⇒cos2α=0Consider the expression cosα+cosβ+cosγ2=0+cosβ+sinβ2=cos2β+sin2β+2cosβsinβ=1+sin2βTherefore, the required expression is1+sin2β