If cos(A + B) = 4/5 and sin(A - B) = 5/13 and A,B lies between 0 and pi/4

Question

 find the value of tan2A?  

 

 

Answer 1

A,B lies between 0 and pi/4.

In first quadrant 6 trigonometric ratios are positive.

From the pythagorean theorem hypotenuse is 5 and adjacent side is 4, then opposite side is 3.

From the pythagorean theorem hypotenuse is 13 andopposite side is 5, then adjacent side is 12.