Answer:
-84
Step-by-step explanation:
Answer:
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)} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B1%7D%7Bcos%28x%29%7D%20-%20%5Cfrac%7B1%7D%7Bsin%28x%29%7D%20%20%7D%7B%5Cfrac%7B1%7D%7Bsin%28x%29%7D%20%2A%20%5Cfrac%7B1%7D%7Bcos%28x%29%7D%20%20%7D)
Simplify the denominator:
![\frac{\frac{1}{cos(x)} - \frac{1}{sin(x)} }{\frac{1}{cos(x)sin(x)} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B1%7D%7Bcos%28x%29%7D%20-%20%5Cfrac%7B1%7D%7Bsin%28x%29%7D%20%20%7D%7B%5Cfrac%7B1%7D%7Bcos%28x%29sin%28x%29%7D%20%20%7D)
Simplify the numerator:
![\frac{{\frac{2(sin(x)-cos(x))}{sin(2x)} } }{\frac{1}{sin(x)} * \frac{1}{cos(x)} }](https://tex.z-dn.net/?f=%5Cfrac%7B%7B%5Cfrac%7B2%28sin%28x%29-cos%28x%29%29%7D%7Bsin%282x%29%7D%20%7D%20%20%7D%7B%5Cfrac%7B1%7D%7Bsin%28x%29%7D%20%2A%20%5Cfrac%7B1%7D%7Bcos%28x%29%7D%20%20%7D)
Divide the fractions: <u>(a/b)/(c/d) = (a * d)/(b * c)</u>:
![\frac{(-cos(x)+sin(x))*2cos(x)sin(x)}{sin(2x)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28-cos%28x%29%2Bsin%28x%29%29%2A2cos%28x%29sin%28x%29%7D%7Bsin%282x%29%7D)
Use the identity: <u>2cos(x)sin(x) = sin(2x):</u>
![\frac{sin(2x)(-cos(x)+sin(x))}{sin(2x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%282x%29%28-cos%28x%29%2Bsin%28x%29%29%7D%7Bsin%282x%29%7D)
Cancel out the common factor (sin(2x)):
-cos(x) + sin(x)
Simplify:
sin(x) - cos(x)
3 & 6 - LCM = 3. 3's multiples are 3, 6, 9,12, 16, etc. 6's multiples are 6, 12, 18, etc. therefore, the least common multiple is 6.
GCF - 3's factors are 1, 3, and 6's factors 1, 2, 3. so the greatest common factor is 3.
Answer:
97
Step-by-step explanation:
Answer:
July 28, 1914--World War 1
Step-by-step explanation: