Answer:
sin(x)-cos(x)
Step-by-step explanation:
[tex]\frac{\frac{1}{cos(x)} - \frac{1}{sin(x)} }{\frac{1}{sin(x)} * \frac{1}{cos(x)} }[/tex]
Simplify the denominator:
[tex]\frac{\frac{1}{cos(x)} - \frac{1}{sin(x)} }{\frac{1}{cos(x)sin(x)} }[/tex]
Simplify the numerator:
[tex]\frac{{\frac{2(sin(x)-cos(x))}{sin(2x)} } }{\frac{1}{sin(x)} * \frac{1}{cos(x)} }[/tex]
Divide the fractions: (a/b)/(c/d) = (a * d)/(b * c):
[tex]\frac{(-cos(x)+sin(x))*2cos(x)sin(x)}{sin(2x)}[/tex]
Use the identity: 2cos(x)sin(x) = sin(2x):
[tex]\frac{sin(2x)(-cos(x)+sin(x))}{sin(2x)}[/tex]
Cancel out the common factor (sin(2x)):
-cos(x) + sin(x)
Simplify:
sin(x) - cos(x)
