Mathematics: Sec theta - csc theta / (csc theta)(sec theta)

Sec theta - csc theta / (csc theta)(sec theta)

veronicatrejoaguiler

11.01.2022

sin(x)-cos(x)

Step-by-step explanation:

$\frac{\frac{1}{cos(x)} - \frac{1}{sin(x)} }{\frac{1}{sin(x)} * \frac{1}{cos(x)} }$

Simplify the denominator:

$\frac{\frac{1}{cos(x)} - \frac{1}{sin(x)} }{\frac{1}{cos(x)sin(x)} }$

Simplify the numerator:

$\frac{{\frac{2(sin(x)-cos(x))}{sin(2x)} } }{\frac{1}{sin(x)} * \frac{1}{cos(x)} }$

Divide the fractions: (a/b)/(c/d) = (a * d)/(b * c):

$\frac{(-cos(x)+sin(x))*2cos(x)sin(x)}{sin(2x)}$

Use the identity: 2cos(x)sin(x) = sin(2x):

$\frac{sin(2x)(-cos(x)+sin(x))}{sin(2x)}$

Cancel out the common factor (sin(2x)):

-cos(x) + sin(x)

Simplify:

sin(x) - cos(x)

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