InterviewSolution
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InterviewSolution
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If `sin alpha + sin beta = a and cos alpha + cos beta =b`, show that `sin(alpha+beta)=(2ab)/(alpha^2+beta^2)` |
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Answer» `Sin(alpha) + Sin(beta)=a``Cos(alpha) + cos(beta)=b``2Sin((alpha +beta)/2)Cos((alpha-beta)/2)=a``2cos((alpha+beta)/2)cos((alpha-beta)/2)=b`then, `tan((alpha+beta)/2)= a/b` By using angles of triangle, `Sin((alpha+beta)/2)=a/sqrt(a^2+b^2)` `cos((alpha+beta)/2)= b/sqrt(a^2+b^2)` Hence, `Sin(alpha+beta)=2Sin((alpha+beta)/2)cos((alpha+beta)/2)``= (2ab)/(a^2+b^2)` |
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