Buktikan identitas trigonometri sin 2x+cos2x+1/sin x = 2 cot x (sin x+cos x)

[tex] \frac{sin2x + cos2x + 1}{sinx} = 2cotx(sinx + cosx) [/tex]

Ubah ruas kiri agar menjadi sama dengan ruas kanan

[tex] 2 cot x (sin x + cos x) \\ = \frac{2 cos x}{sin x} (sin x + cos x) \\ = \frac{2 sin x cos x}{sin x} + \frac{2 cos^2 x}{sin x} \\ = \frac{sin 2x}{sin x} + \frac{(2 cos^2 x - 1) + 1}{sin x} \\ = \frac{sin 2x}{sin x} + \frac{cos 2x + 1}{sin x} \\ = \frac{sin 2x + cos 2x + 1}{sin x} [/tex]

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