Question

If tan(x+y)=3/4 and tan(x-y)=8/15 find tan 2x,tan 2y

Answer 1

tan(x+y)=3/4, tan(x-y)= 8/15 find tan2x and 2y

tan(u+v)=(tan(u)+tan(v))/(1-tanutanv)

tan(u-v)=(tan(u)-tan(v))/(1+tanutanv)

tan(u)+tan(v)= tan(u+v)(1-tanutanv)

tan(u)-tan(v)= tan(u-v)(1+tanutanv)

Substitute u=x+y, v=x-y

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

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

Now you can plug in values for tan(x+y) and tan(x-y) and find tan(2x) and tan(2y).

(3/4)+(8/15)=2x

2x=77÷15