In a right angled triangle, acute angle A and B satisfy `tanA+tanB+tan^2A+tan^2B+tan^3A+tan^3B=70.` Find the angle A and B in radians.

Explanation

`A+B+90=180`

`A+B=90`

`B=90-A`

`tanB=tan(90-A)=cotA`

`tanB=1/(tanA)`

`(tanA+1/tanA)+(tan^2A+1/tan^2A)+(tan^3A+1/tan^3A)=70`

`(tanA+1/tanA)+(tanA+1/tanA)^2-2+(tanA+1/tanA)^3-3(tanA+1/tanA)=70`

Let`tanA+1/tanA=t`

...