Matematika

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bentuk identitas cosx/sinx - 1/cosxsinx =-tanx
bentuk identitas cosx/sinx - 1/cosxsinx =-tanx

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  • [tex]a) \frac{cos x}{sin x} - \frac{1}{cos x . sin x} = - tan x[/tex]

    [tex] \frac{ cos^{2} x - 1}{cos x . sin x} = - tan x[/tex]

    [tex] \frac{- sin^{2} x}{cos x . sin x} = - tan x[/tex]

    [tex] \frac{- sin x}{cos x} = tan x[/tex]

    - tan x = - tan x     ... terbukti

    [tex]b) \frac{sin x - cos x}{sin x + cos x} = \frac{tan x - 1}{tan x + 1} [/tex]
      
       [tex] \frac{cos x ( \frac{sin x}{cos x} - 1)}{cos x ( \frac{sin x}{cos x} + 1)} = \frac{tan x - 1}{tan x + 1} [/tex]
     
      [tex] \frac{ \frac{sin x}{cos x} - 1}{ \frac{sin x}{cos x} + 1} = \frac{tan x - 1}{tan x + 1} [/tex]

    [tex] \frac{tan x - 1}{tan x + 1} = \frac{tan x - 1}{tan x - 1} [/tex]
                   terbukti

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