Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = π → C = π - (A + B)
→ sin C = sin(π - (A + B)) cos C = sin(π - (A + B))
→ sin C = sin (A + B) cos C = - cos(A + B)
Use the following Sum to Product Identity:
sin A + sin B = 2 cos[(A + B)/2] · sin [(A - B)/2]
cos A + cos B = 2 cos[(A + B)/2] · cos [(A - B)/2]
Use the following Double Angle Identity:
sin 2A = 2 sin A · cos A
<u>Proof LHS → RHS</u>
LHS: (sin 2A + sin 2B) + sin 2C
![\text{Factor:}\qquad \qquad \qquad 2\sin C\cdot [\cos (A-B)+\cos (A+B)]](https://tex.z-dn.net/?f=%5Ctext%7BFactor%3A%7D%5Cqquad%20%5Cqquad%20%5Cqquad%202%5Csin%20C%5Ccdot%20%5B%5Ccos%20%28A-B%29%2B%5Ccos%20%28A%2BB%29%5D)
LHS = RHS: 4 cos A · cos B · sin C = 4 cos A · cos B · sin C 
Answer:
By AA similarity
Step-by-step explanation:
We have been given that ABCD is a parallelogram
So, by the property of parallelogram AB ||CD and FD is cutting the line BC
Hence, FD is transverse line. In transverse line alternate angles are equal.
Therefore, ∠AFD=∠EDC (alternate interior angles)
And ∠FAD=∠ECD (opposite angles in parallelogram)
Therefore, by AA similarity △ADF∼△CDE
What's Ratinal? Do you mean rational? If so, you're right.
Answer:
x = 90°
Step-by-step explanation:
Hello!
The sum of angles on a straight line is 180°.
To find the value of angle x°, we can subtract all the given angles form 180°.
<h3>Find x</h3>
- 180° - 60° - 30° = x°
- 180° - 90° = x°
- 90° = x°
The value of x is 90°.
So let's pretend there is olives, pepperoni, jalapenos, sausage, and pineapple. Here is an example of an outcome chart that is useful when it comes to these type of problems.
sausage
l
pineapple-olives-pepperoni
l
jalapenos
1. Olives and sausages
2. olives and pepperoni
3. olives and jalapenos
4. olives and pineapple
5. sausages and pepperoni
6. sausages and jalapenos
7. sausage and pineapple
8. pepperoni and jalapenos
9. pepperoni and pineapple
10. pineapple and jalapenos
There are 10 total 2 topping pizzas possible.
Now I'm hungry...
Hope this helps!
