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In a right angled triangle, acute angle ...

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.

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`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`
...
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