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Linear Functions

If 0 < _ alfa...

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If 0 < _ alfa , beta < _ 90 degree and tan ( alfa + beta )=3 & tan (alfa - beta)=2 Then find sin 2alfa =? A) -1/(root 2) B) 1/(root 2) C)1/2. D) none of these

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\tan α = \frac{1 - \cos β}{\sin β}

\tan 3 α = \tan 2 β

\tan 2 α = \tan β

\tan 2 β = \tan α

(d) none of these

x_{1}, x_{2}, x_{3}, x_{4}

are roots of the equation

x^{4} - x^{3} s i n 2 β + x^{2} c o s 2 β - x c o s β - s i n β = 0

t a n^{- 1} x_{1} + t a n^{- 1} x_{2} + t a n^{- 1} x_{3} + t a n^{- 1} x_{4} =

2 \tan α = 3 \tan β, then \tan (α - β) =

\frac{\sin 2 β}{5 - \cos 2 β}

\frac{\cos 2 β}{5 - \cos 2 β}

\frac{\sin 2 β}{5 + \cos 2 β}

(d) none of these

x_{1}, x_{2}, x_{3}, x_{4}

are roots of the equation

x^{4} - x^{3} s i n 2 β + x^{2} c o s 2 β - x c o s β - s i n β = 0

t a n^{- 1} x_{1} + t a n^{- 1} x_{2} + t a n^{- 1} x_{3} + t a n^{- 1} x_{4} =

tan θ_{1}, tan θ_{2}, tan θ_{3}, tan θ_{4}

are the roots of the equation

x^{4} - x^{3} sin 2 β + x^{2} cos 2 β - x cos β - sin β = 0

tan (θ_{1} + θ_{2} + θ_{3} + θ_{4}) =

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