Find tan(alpha)

tan(α + β)=7...........1)
tan(α - β)=5................2)
_____________________________

from 1) and 2) we have

α + β=tan^-1(7).........1a)
α - β=tan^-1(5).............2a)
___________________________add both
α + β+α - β =tan^-1(7)+tan^-1(5)
2α =2.8023
α =2.8023/2
α =1.40115...(result in radians)


α + β=tan^-1(7).........1a) , substitute α =1.40115

1.40115+ β=tan^-1(7)
β=tan^-1(7)-1.40115
β=0.0277493...(result in radians)


=> tan(α)=tan(1.40115)=5.83796...(result in radians)

 

Very good.