If α , β , γ ∈ [ 0 , π ] and if α , β , γ are in AP, then c o s γ − c o s α s i n α − s i n γ is equal to

Question

If α , β , γ ∈ [ 0 , π ] and if α , β , γ are in AP, then c o s γ − c o s α s i n α − s i n γ ​ is equal to

TestHub · Accepted Answer

c o s γ − c o s α s i n α − s i n γ ​ = 2 s i n 2 α + γ ​ ⋅ s i n 2 α − γ ​ 2 c o s 2 α + γ ​ s i n 2 α − γ ​ ​ = cot 2 α + γ ​ [ ∵ sin A − sin B = 2 cos ( 2 A + B ​ ) sin ( 2 A − B ​ ) and cos A − cos B = 2 sin ( 2 A + B ​ ) sin ( 2 B − A ​ ) ​ ] But α , β , γ are in A P ⇒ 2 α + γ ​ = β So, required value is cot β .

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JEE Main 2027 (Class 12+)