Question

if 2 tanA=cotB then show that cos(A-B)=3cos(A+B)​

Answer 1

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2 tan A = cot B

2sinA/cos A=cos B/sinB

2sinAsinB=cosAcosB

Cos(A-B)=cosAcosB+sinAsinB

=2sinAsinB+sinAsinB

=3sinAsinB

=3(2sinAsinB-sinAsinB)

3(cosAcosB-sinAsinB)

3cos(A+B)