Buktikan identitas 2 tan X / 1 + tan² X = 2 sin X cos X

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Buktikan identitas
2 tan X / 1 + tan² X = 2 sin X cos X

Jawaban Terkonfirmasi

frac{2 tan x}{1 + tan^2 x} = 2 sin x cos x

Ruas kiri:
frac{2 tan x}{1 + tan^2 x} = frac{2 frac{sin x}{cos x}}{1 + frac{sin^2 x}{cos^2 x}}
frac{2 tan x}{1 + tan^2 x} = frac{2 frac{sin x}{cos x}}{frac{cos^2 x + sin^2 x}{cos^2 x}}
frac{2 tan x}{1 + tan^2 x} = frac{2 sin x}{frac{cos^2 x + sin^2 x}{cos x}}
frac{2 tan x}{1 + tan^2 x} = frac{2 sin x}{frac{1}{cos x}}
frac{2 tan x}{1 + tan^2 x} = 2 sin x cos x
TERBUKTI

semoga membantu 🙂

Jawaban Terkonfirmasi

frac{2 tanx}{1+ tan^{2} x}=frac{2 tanx}{1+ frac{sin^{2}x}{cos^2 x}} \ \ frac{2 tanx}{(cos^x+sin^x)/cos^2x}} = 2 tan x . cos^2 x = 2 sinx / cos x . cos^2x=2sinx.cosx