identitas trigonometri
sin² x + cos² x = 1
Ingat :
a² - b² = (a + b)(a - b)
1 - 2 cos² x
= sin² x + cos² x - 2 cos² x
= sin² x - cos² x
= (sin x + cos x)(sin x - cos x)
•
1 + 2 sin x cos x = (sin x + cos x)²
[tex] \frac{1 \: - \: {2 \: cos}^{2} x}{1 \: + \: 2 \: sin \: x \: cos \: x} \\ \\ = \: \frac{(sin \: x \: + \: cos \: x)(sin \: x \: - \: cos \: x)}{ {(sin \: x \: + \: cos \: x)}^{2} } \\ \\ = \: \boxed{ \frac{sin \: x \: - \: cos \: x}{sin \: x \: + \: cos \: x} }[/tex]
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identitas trigonometri
sin² x + cos² x = 1
Ingat :
a² - b² = (a + b)(a - b)
1 - 2 cos² x
= sin² x + cos² x - 2 cos² x
= sin² x - cos² x
= (sin x + cos x)(sin x - cos x)
•
1 + 2 sin x cos x = (sin x + cos x)²
•
[tex] \frac{1 \: - \: {2 \: cos}^{2} x}{1 \: + \: 2 \: sin \: x \: cos \: x} \\ \\ = \: \frac{(sin \: x \: + \: cos \: x)(sin \: x \: - \: cos \: x)}{ {(sin \: x \: + \: cos \: x)}^{2} } \\ \\ = \: \boxed{ \frac{sin \: x \: - \: cos \: x}{sin \: x \: + \: cos \: x} }[/tex]