Answer:
Step-by-step explanation:
Formulas used:
![sin( A +B) = 2sin Acos B\\\\sin A= sin (\frac{A}{2} + \frac{A}{2}) = 2 \ sin \frac{A}{2}cos \frac{A}{2}\\\\cos(A + B) = cosA cosB - sinA sinB\\\\cos A = cos(\frac{A}{2} + \frac{A}{2}) = cos \frac{A}{2} cos \frac{A}{2} - sin \frac{A}{2} sin \frac{A}{2}](https://tex.z-dn.net/?f=sin%28%20A%20%2BB%29%20%3D%202sin%20Acos%20B%5C%5C%5C%5Csin%20A%3D%20sin%20%28%5Cfrac%7BA%7D%7B2%7D%20%2B%20%5Cfrac%7BA%7D%7B2%7D%29%20%3D%202%20%5C%20sin%20%5Cfrac%7BA%7D%7B2%7Dcos%20%5Cfrac%7BA%7D%7B2%7D%5C%5C%5C%5Ccos%28A%20%2B%20B%29%20%3D%20cosA%20cosB%20-%20sinA%20sinB%5C%5C%5C%5Ccos%20A%20%3D%20cos%28%5Cfrac%7BA%7D%7B2%7D%20%2B%20%5Cfrac%7BA%7D%7B2%7D%29%20%3D%20cos%20%5Cfrac%7BA%7D%7B2%7D%20cos%20%5Cfrac%7BA%7D%7B2%7D%20%20-%20sin%20%5Cfrac%7BA%7D%7B2%7D%20sin%20%5Cfrac%7BA%7D%7B2%7D)
![= cos^2 \frac{A}{2} - sin^2 \frac{A}{2}](https://tex.z-dn.net/?f=%3D%20cos%5E2%20%5Cfrac%7BA%7D%7B2%7D%20-%20sin%5E2%20%5Cfrac%7BA%7D%7B2%7D)
![1 - sin^2 \frac{A}{2} = cos^2 \frac{A}{2}](https://tex.z-dn.net/?f=1%20-%20sin%5E2%20%5Cfrac%7BA%7D%7B2%7D%20%3D%20cos%5E2%20%5Cfrac%7BA%7D%7B2%7D)
![\frac{sin\frac{A}{2}}{cos\frac{A}{2}} = tan\frac{A}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%5Cfrac%7BA%7D%7B2%7D%7D%7Bcos%5Cfrac%7BA%7D%7B2%7D%7D%20%3D%20tan%5Cfrac%7BA%7D%7B2%7D)
Given :
LHS =
![\frac{sin \frac{A}{2} + sin A }{1 + cos \frac{A}{2} + cosA}\\\\=\frac{sin \frac{A}{2} + 2sin \frac{A}{2} cos \frac{A}{2} }{1 + cos \frac{A}{2} +cos ^2\frac{A}{2} -sin^2 \frac{A}{2} }\\\\= \frac{sin\frac{A}{2}( 1 +2cos \frac{A}{2} ) }{cos \frac{A}{2} + cos ^2 \frac{A}{2} + 1 - sin^2\frac{A}{2} }\\\\= \frac{sin\frac{A}{2}( 1 +2cos \frac{A}{2} ) }{cos \frac{A}{2} + cos ^2 \frac{A}{2} +cos ^2 \frac{A}{2} }\\\\](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%20%5Cfrac%7BA%7D%7B2%7D%20%2B%20sin%20A%20%7D%7B1%20%2B%20cos%20%5Cfrac%7BA%7D%7B2%7D%20%20%2B%20cosA%7D%5C%5C%5C%5C%3D%5Cfrac%7Bsin%20%5Cfrac%7BA%7D%7B2%7D%20%2B%202sin%20%5Cfrac%7BA%7D%7B2%7D%20cos%20%5Cfrac%7BA%7D%7B2%7D%20%20%7D%7B1%20%2B%20cos%20%5Cfrac%7BA%7D%7B2%7D%20%2Bcos%20%5E2%5Cfrac%7BA%7D%7B2%7D%20-sin%5E2%20%5Cfrac%7BA%7D%7B2%7D%20%7D%5C%5C%5C%5C%3D%20%5Cfrac%7Bsin%5Cfrac%7BA%7D%7B2%7D%28%201%20%2B2cos%20%5Cfrac%7BA%7D%7B2%7D%20%29%20%7D%7Bcos%20%5Cfrac%7BA%7D%7B2%7D%20%20%2B%20cos%20%5E2%20%5Cfrac%7BA%7D%7B2%7D%20%2B%201%20-%20sin%5E2%5Cfrac%7BA%7D%7B2%7D%20%7D%5C%5C%5C%5C%3D%20%5Cfrac%7Bsin%5Cfrac%7BA%7D%7B2%7D%28%201%20%2B2cos%20%5Cfrac%7BA%7D%7B2%7D%20%29%20%7D%7Bcos%20%5Cfrac%7BA%7D%7B2%7D%20%20%2B%20cos%20%5E2%20%5Cfrac%7BA%7D%7B2%7D%20%2Bcos%20%5E2%20%5Cfrac%7BA%7D%7B2%7D%20%20%20%7D%5C%5C%5C%5C)
![=\frac{sin\frac{A}{2}( 1 +2cos \frac{A}{2} ) }{cos \frac{A}{2} + 2cos ^2 \frac{A}{2} }\\\\=\frac{sin\frac{A}{2}( 1 +2cos \frac{A}{2} ) }{cos \frac{A}{2} ( 1 + 2cos \frac{A}{2}) }\\\\=\frac{sin\frac{A}{2}}{cos\frac{A}{2}}\\\\= tan \frac{A}{2}\\\\= RHS](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bsin%5Cfrac%7BA%7D%7B2%7D%28%201%20%2B2cos%20%5Cfrac%7BA%7D%7B2%7D%20%29%20%7D%7Bcos%20%5Cfrac%7BA%7D%7B2%7D%20%20%2B%202cos%20%5E2%20%5Cfrac%7BA%7D%7B2%7D%20%7D%5C%5C%5C%5C%3D%5Cfrac%7Bsin%5Cfrac%7BA%7D%7B2%7D%28%201%20%2B2cos%20%5Cfrac%7BA%7D%7B2%7D%20%29%20%7D%7Bcos%20%5Cfrac%7BA%7D%7B2%7D%20%28%201%20%20%2B%202cos%20%5Cfrac%7BA%7D%7B2%7D%29%20%7D%5C%5C%5C%5C%3D%5Cfrac%7Bsin%5Cfrac%7BA%7D%7B2%7D%7D%7Bcos%5Cfrac%7BA%7D%7B2%7D%7D%5C%5C%5C%5C%3D%20tan%20%5Cfrac%7BA%7D%7B2%7D%5C%5C%5C%5C%3D%20RHS)
Answer:
B: 4
Step-by-step explanation:
#first
Answer:
Infinitely many solutions
Step-by-step explanation:
By multiplying the entire top equation by two, you'll find that both of these equations are actually technically the same, meaning that there are infinitely many solutions to this system.
Answer:
-486, 1458, -4374, 13,122
Step-by-step explanation:
each number is multiplied by -3
<h3>
Answer: B) the function g(x) has a larger slope</h3>
===================================================
Explanation:
The slope of f(x) is 4, since the equation y = 4x+2 has slope m = 4. Compare this to y = mx+b.
The slope of g(x) is 5. Note how if we started at (0,-2) on the red line and moved up 5 and to the right 1, we arrive at (1,3) which is another point on the red line. You could use the slope formula
m = (y2-y1)/(x2-x1)
to get the same result.
Since the slope of f(x) is 4 and the slope of g(x) is 5, we see that g(x) has a larger slope. The g(x) line is steeper compared to f(x).