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Property 6

if tan alpha ...

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if tan alpha and tan beta be the roots of x^2 - px + q =0 then find cos2(alpha+beta)

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tan α

tan β

are the roots of the equation

x^{2} + p x + q = 0 (p \neq 0)

tan α

tan β

are the roots of

x^{2} - p x + q = 0

, then find the value of

{sin}^{2} (α + β)

tan α, tan β

are the roots of the equation

x^{2} + p x + q = 0 (p \neq 0)

{sin}^{2} (α + β) + p sin (α + β) cos (α + β) + q {cos}^{2} (α + β) =

tan α, t a n β

are the roots of the equation

x^{2} + p x + q = 0 (p \neq 0)

α, β

be the roots of the equation

x^{2} - p x + q = 0

α > 0, β > 0,

then find the value of

α^{5} + β^{5}

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