Let L=sin2(α+β)+3sin(α+β)cos(α+β)+4cos2(α+β) where tanα and tanβ are the roots of the quadratic equation t2+3t+4=0, M=sin2α+sin2β+sin2γ−2cosαcosβcosγ where α+β+γ=π and N=cotαcotγ where cotα,cotβ and cotγ are in arithmetic progression and α+β+γ=π2. Then the value of (L+M+N) is

Let L=sin2(α+β)+3sin(α+β)cos(α+β)+4cos2(α+β) where tanα and t

1.	Let L=sin2(α+β)+3sin(α+β)cos(α+β)+4cos2(α+β) where tanα and tanβ are the roots of the quadratic equation t2+3t+4=0, M=sin2α+sin2β+sin2γ−2cosαcosβcosγ where α+β+γ=π and N=cotαcotγ where cotα,cotβ and cotγ are in arithmetic progression and α+β+γ=π2. Then the value of (L+M+N) is
Answer» Let $L = {sin}^{2} (α + β) + 3 sin (α + β) cos (α + β) + 4 {cos}^{2} (α + β)$ where $tan α$ and $tan β$ are the roots of the quadratic equation $t^{2} + 3 t + 4 = 0,$ $M = {sin}^{2} α + {sin}^{2} β + {sin}^{2} γ - 2 cos α cos β cos γ$ where $α + β + γ = π$ and $N = cot α cot γ$ where $cot α, cot β$ and $cot γ$ are in arithmetic progression and $α + β + γ = \frac{π}{2} .$ Then the value of $(L + M + N)$ is