This is not an identity.
![\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} \neq \sec(x)](https://tex.z-dn.net/?f=%5Cdfrac%7B2%28%5Ccos%28x%29%5Csin%28x%29%20-%20%5Csin%28x%29%5Ccos%282x%29%29%7D%7B%5Csin%282x%29%7D%20%5Cneq%20%5Csec%28x%29)
Check x = π/4, for which we have cos(π/4) = sin(π/4) = 1/√2. Together with sin(2•π/4) = sin(π/2) = 1 and cos(2•π/4) = cos(π/2) = 0, the left side becomes 1, while sec(π/4) = 1/cos(π/4) = √2.
Keeping the left side unchanged, the correct identity would be
![\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} = -2\cos(x) + 1 + \sec(x)](https://tex.z-dn.net/?f=%5Cdfrac%7B2%28%5Ccos%28x%29%5Csin%28x%29%20-%20%5Csin%28x%29%5Ccos%282x%29%29%7D%7B%5Csin%282x%29%7D%20%3D%20-2%5Ccos%28x%29%20%2B%201%20%2B%20%5Csec%28x%29)
To show this, recall
• sin(2x) = 2 sin(x) cos(x)
• cos(2x) = cos²(x) - sin²(x)
• cos²(x) + sin²(x) = 1
Then we have
![\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} = \dfrac{2\cos(x)\sin(x) - 2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = \dfrac{\sin(2x) - 2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = 1 - \dfrac{2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = 1 - \dfrac{2\sin(x)(\cos^2(x) - \sin^2(x))}{2 \sin(x)\cos(x)} \\\\ = 1 - \dfrac{\cos^2(x) - \sin^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \dfrac{\sin^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \dfrac{1 - \cos^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \sec(x) - \cos(x) \\\\ = -2\cos(x) + 1 + \sec(x)](https://tex.z-dn.net/?f=%5Cdfrac%7B2%28%5Ccos%28x%29%5Csin%28x%29%20-%20%5Csin%28x%29%5Ccos%282x%29%29%7D%7B%5Csin%282x%29%7D%20%3D%20%5Cdfrac%7B2%5Ccos%28x%29%5Csin%28x%29%20-%202%5Csin%28x%29%5Ccos%282x%29%7D%7B%5Csin%282x%29%7D%20%5C%5C%5C%5C%20%3D%20%5Cdfrac%7B%5Csin%282x%29%20-%202%5Csin%28x%29%5Ccos%282x%29%7D%7B%5Csin%282x%29%7D%20%5C%5C%5C%5C%20%3D%201%20-%20%5Cdfrac%7B2%5Csin%28x%29%5Ccos%282x%29%7D%7B%5Csin%282x%29%7D%20%5C%5C%5C%5C%20%3D%201%20-%20%5Cdfrac%7B2%5Csin%28x%29%28%5Ccos%5E2%28x%29%20-%20%5Csin%5E2%28x%29%29%7D%7B2%20%5Csin%28x%29%5Ccos%28x%29%7D%20%5C%5C%5C%5C%20%3D%201%20-%20%5Cdfrac%7B%5Ccos%5E2%28x%29%20-%20%5Csin%5E2%28x%29%7D%7B%5Ccos%28x%29%7D%20%5C%5C%5C%5C%20%3D%201%20-%20%5Ccos%28x%29%20%2B%20%5Cdfrac%7B%5Csin%5E2%28x%29%7D%7B%5Ccos%28x%29%7D%20%5C%5C%5C%5C%20%3D%201%20-%20%5Ccos%28x%29%20%2B%20%5Cdfrac%7B1%20-%20%5Ccos%5E2%28x%29%7D%7B%5Ccos%28x%29%7D%20%5C%5C%5C%5C%20%3D%201%20-%20%5Ccos%28x%29%20%2B%20%5Csec%28x%29%20-%20%5Ccos%28x%29%20%5C%5C%5C%5C%20%3D%20-2%5Ccos%28x%29%20%2B%201%20%2B%20%5Csec%28x%29)
12 x 46 = 552
5 x 380 = 1900
552 x 3.44 = 1900
You will need 4 Cases
The answer is 30 because 180-150 equals 30
Answer: ![\frac{7w+7}{8}+\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B7w%2B7%7D%7B8%7D%2B%5Cfrac%7B3%7D%7B4%7D)
Step-by-step explanation:
![\frac{7}{8}\left(w+1\right)+\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B8%7D%5Cleft%28w%2B1%5Cright%29%2B%5Cfrac%7B3%7D%7B4%7D)
![\frac{7}{8}w+1\cdot \frac{7}{8}+\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B8%7Dw%2B1%5Ccdot%20%5Cfrac%7B7%7D%7B8%7D%2B%5Cfrac%7B3%7D%7B4%7D)
Answer:
-0.4522
Step-by-step explanation: