If tan Alpha Banten beta be the roots of x square - 3 x + 2 is equal to zero then find cos 2 (alpha + beta)

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Q. If

α

and

β

(α > β)

are the roots of the equation

x^{2} - \sqrt{2} x + \sqrt{3 - 2 \sqrt{2}} = 0,

then the value of

({cos}^{- 1} α + {tan}^{- 1} α + {tan}^{- 1} β)

is equal to

If $t a n α, t a n β$ are the roots of the equation $x^{2}$ + ax + b = 0 then the value of $s i n^{2} (α + β) + a s i n (α + β) c o s (α + β) + b c o s^{2} (α + β) =$

Q.
If

tan α, tan β

are the roots of the equation

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

then

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

tan α

and

tan β

are the roots of the equation

x^{2} + a x + b = 0

then the value of

{sin}^{2} (α + β) + a sin (α + β) cos (α + β) + b {cos}^{2} (α + β)

is equal to

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