coltonhayden88
coltonhayden88 coltonhayden88
  • 25-06-2022
  • Mathematics
contestada

How do I simplify the following expression by writing it as a term with only one trigonometric function?

(4-2sec^2(x))/(sec^2(x))

Respuesta :

surjithayer surjithayer
  • 25-06-2022

Answer:

2 cos (2x)

Step-by-step explanation:

[tex]\frac{4 -2 sec^2x}{sec^2x} \\=\frac{4-\frac{2}{cos^2x} }{\frac{1}{cos^2 x} } \\=\frac{\frac{4 cos^2x-2}{cos^2 x} }{\frac{1}{cos^2x} } \\=\frac{2(2 cos^2x-1)}{cos^2x} \times \frac{cos^2x}{1} \\=2(2cos^2x-1)\\=2cos(2x)[/tex]

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