Answer :

Given sin α sin β – cos α cos β + 1 = 0


-(cos α cos β – sin α sin β) + 1 = 0


We know that cos(A +B) = cosA cosB - sinA sinB


-cos(α + β) + 1 = 0


cos(α + β) = 1


We know that sin θ = √(1 – cos2 θ)


sin(α + β) = 0 …(1)


Consider 1 + cot α tan β,




We know that sin(A ±B) = sinA cosB ± cosA sinB



= 0 = RHS


Hence, proved.


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