cosA=5/13 sinB=15/17 find tan(A+B)

Question

find tan(A+B)

Answer 1

Cos  A  =5/13

 

 So Sin A = 12/13

 

so Tan A = 12/5

 

sin B =15/17

 

So cos B = 8/17

 

Tan B =15/8

 

tan(A+B) = ( tan A - tan B) / ( 1 + tan A tan B)

 

               =(12/5 -15/8 ) /( 1 + 12/5 * 15/8)

 

               =[(96 -75)/ 40 ]/ ( 1 +  9/2)

                =( 21/40 ) / 11/2

                =21/40 * 2/11

                =21/220