Prove that :cos2α+cos2(α+β)−2cosαco...
Question

# Prove that ( : cos ^{2} alpha+cos ^{2}(alpha+beta)-2 cos alpha cos beta cos (alpha+beta)=sin ^{2} beta )

JEE/Engineering Exams
Maths
Solution
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( cos ^{2} alpha+cos ^{2}(alpha+beta)-2 cos alpha cos beta cos (alpha+beta) )
( Gamma cos (A+B)=cos A cos B+sin A sin B_{1} )
( cos ^{2} alpha+(cos alpha cos beta+sin alpha sin beta)^{2}-2 cos alpha cos _{beta} )
( C cos alpha cos beta+sin alpha sin beta) )
( cos ^{2} alpha+cos ^{2} alpha cos ^{2} beta+sin ^{2} alpha sin ^{2} beta+2 cos alpha cos beta )
( sin alpha sin beta-2 cos ^{2} alpha cos ^{2} beta-2 cos alpha sin alpha cos beta sin beta )
( cos ^{2} alpha-cos ^{2} alpha cos ^{2} beta+sin ^{2} alpha sin ^{2} beta )
( cos ^{2} alphaleft(1-cos ^{2} betaright)+sin ^{2} alpha sin ^{2} beta )
( cos ^{2} alphaleft(sin ^{2} betaright)+sin ^{2} alpha sin ^{2} beta )
( sin ^{2} betaleft(cos ^{2} alpha+sin ^{2} alpharight) )
( sin ^{2} beta(1)=sin ^{2} beta )

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