Question

​If tan(x+y)=5/3 and tan(x-y)=7/23,find tan 2x?

Answer 1

tan (x+y) = 5/3 
tan(x-y) = 7/23

tan 2x = tan ( (x+y) + (x-y) )
therefore
tan 2x = tan(x+y) + tan (x-y) / 1 - tan(x+y) tan(x-y)

hence, tan 2x = 5/3 + 7/23 / 1 - 5/3 * 7/23
 = 115+21/69 / 69-35/69
= 136/34
= 68/17. 
therefore tan 2x = 68/17