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Trigonometry

A and B are acute angles such that sin(A-B)=1/2 and sin A cos B= 7/10. Without using a calculator, find the value of tanA/tanB.
 
 
 
Ans: 7/2
 
 
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1 Answer

 
 
sin(A-B)=1/2
sinAcosB=7/10
 
sin(A-B)=sinAcosB-cosAsinB
 
 
1/2=7/10-cosAsinB
cosAsinB=7/10-1/2=7/10-5/10=2/10
 
tanA/tanB=sinA/cosA
                sinB/cosB
              =sinAcosB=7/10 =7/2
                cosAsinB   2/10