Trigonometry

Question

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

 

 

Thank you:)

Answer 1

 

 

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