Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B = C → A = C - B
→ B = C - A
Use the Double Angle Identity: cos 2A = 2 cos² A - 1
→ (cos 2A + 1)/2 = cos² A
Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · 2 cos [(A - B)/2]
Use Even/Odd Identity: cos (-A) = cos (A)
<u>Proof LHS → RHS:</u>
LHS: cos² A + cos² B + cos² C
![\text{Sum to Product:}\quad 1+\dfrac{1}{2}\bigg[2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A-2B}{2}\bigg)\bigg]+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\cos (A+B)\cdot \cos (A-B)+\cos^2 C](https://tex.z-dn.net/?f=%5Ctext%7BSum%20to%20Product%3A%7D%5Cquad%201%2B%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%5B2%5Ccos%20%5Cbigg%28%5Cdfrac%7B2A%2B2B%7D%7B2%7D%5Cbigg%29%5Ccdot%20%5Ccos%20%5Cbigg%28%5Cdfrac%7B2A-2B%7D%7B2%7D%5Cbigg%29%5Cbigg%5D%2B%5Ccos%5E2%20C%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D1%2B%5Ccos%20%28A%2BB%29%5Ccdot%20%5Ccos%20%28A-B%29%2B%5Ccos%5E2%20C)
![\text{Factor:}\qquad \qquad 1+\cos C[\cos (A-B)+\cos C]](https://tex.z-dn.net/?f=%5Ctext%7BFactor%3A%7D%5Cqquad%20%5Cqquad%201%2B%5Ccos%20C%5B%5Ccos%20%28A-B%29%2B%5Ccos%20C%5D)
![\text{Sum to Product:}\quad 1+\cos C\bigg[2\cos \bigg(\dfrac{A-B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{A-B-C}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+(C-B)}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-(C-A)}{2}\bigg)](https://tex.z-dn.net/?f=%5Ctext%7BSum%20to%20Product%3A%7D%5Cquad%201%2B%5Ccos%20C%5Cbigg%5B2%5Ccos%20%5Cbigg%28%5Cdfrac%7BA-B%2BC%7D%7B2%7D%5Cbigg%29%5Ccdot%20%5Ccos%20%5Cbigg%28%5Cdfrac%7BA-B-C%7D%7B2%7D%5Cbigg%29%5Cbigg%5D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D1%2B2%5Ccos%20C%5Ccdot%20%5Ccos%20%5Cbigg%28%5Cdfrac%7BA%2B%28C-B%29%7D%7B2%7D%5Cbigg%29%5Ccdot%20%5Ccos%20%5Cbigg%28%5Cdfrac%7B-B-%28C-A%29%7D%7B2%7D%5Cbigg%29)
LHS = RHS: 1 + 2 cos A · cos B · cos C = 1 + 2 cos A · cos B · cos C 
Answer:
acute
Step-by-step explanation:
1. It cannot be right angle as the sides does not satisfy pythagoras theorem.
2. It cannot be obtuse angle as it does not satisfy the rule:
- the length of one side of a triangle must be greater than the differnce and less than the sum of the lengths of the other two sides.
4-3 =1 <6 4+3=7>6
Answer:
x ≥ -1
Step-by-step explanation:
the red fully circle in -1 show that -1 is include
Answer:
Step-by-step explanation:
SOHCAHTOA
O =Opposite
A = Adjacent
H = Hpotenuse
If we draw it out we can see that the opposite side is the UT and adjacent side is SU for ∠S.
When an angle is asked for like here is S so the opposite side of the angle is the opposite side. and the angle close to it is the adjacent. The biggest side is the hypotenuse.
Answer:
D
Step-by-step explanation:
Just multiple them and see which one fits the question.
A: 10 * 8 = 80 * 9 = 720 So it's too big.
B: 9 * 9 = 81 * 9 = 729. Also too big.
C: 9 * 10 = 90 * 9 = 810 too big.
D: 8 * 8 = 64 * 11= 704
