Verify the following identity: [tex]\displaystyle \frac{1+3\cos x-4\cos^3 x}{1-\cos x}=(1+2\cos x)^2[/tex]
Matematika
Anonyme
Pertanyaan
Verify the following identity:
[tex]\displaystyle \frac{1+3\cos x-4\cos^3 x}{1-\cos x}=(1+2\cos x)^2[/tex]
[tex]\displaystyle \frac{1+3\cos x-4\cos^3 x}{1-\cos x}=(1+2\cos x)^2[/tex]
1 Jawaban
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1. Jawaban Anonyme
-4cos³ x + 3cos x + 1
Jumlah koefisien nya = -4 + 3 + 1 = 0
maka : cos x = 1 merupakan slhstu faktor nya
misal : cos x = a
(-4a³ + 3x + 1)/(1 - a)
= (1 - a)(2a + 1)²/(1 - a)
= (2a + 1)²
= (2cos x + 1)²
= ruas kanan
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