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If a/SinA = b/CosA then prove that SinACosA = ab/a 2 + b 2


If    a/SinA = b/CosA   then prove that   SinACosA = ab/a2 + b2


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1 Answers

AskiitiansExpert Abhinav Batra
25 Points
12 years ago

Dear sunny

 

we know by sine rule that

a/sinA=b/sinB=c/sinC

 

futher it is given that

a/sinA=b/cosA

hence b/sinB=b/cosA

So cosA=sinB

cosA=cos(90-B)

hence A+B=90

So C=90

Suppose 

a/sinA=b/sinB=c/sinC=k

sinA=a/k;sinB=b/k;sinC=c/k

so sinA sinB/sin2 C=ab/c2

but we know Sin B =Cos A and c2=a2 +b2 and SinC=1 (since triangle is right angled at C)

so sin A cosA=ab/a2 + b2

 

ALL THE BEST

Abhinav Batra

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