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Find the quadratic equation whose roots ...

Find the quadratic equation whose roots are `tan ((pi)/(8))` and `tan ((5pi)/(8))`?

Text Solution

Verified by Experts

Sum of roots.
`S=tan"" (pi)/(8)+tan ""(5pi)/(8)`
`=tan ""(pi)/(8)+tan ((pi)/(2)+(pi)/(8))`
`=tan ""(pi)/(8)-cot""(pi)/(8)`
`=(sqrt(2)-1)-(sqrt(2)+1)`
`=-2`
Product of roots, `P=(Tan ""(pi)/(8))(tan"" (5pi)/(8))`
`=tan"" (pi)/(8)(-cot""(pi)/(8))`
`=-1`
Hence, the required equation is `x^(2)+2x-1=0`
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cot((pi)/(8))-tan((pi)/(8))=2