Write the left side of the given expression as N/D, where
N = sinA - sin3A + sin5A - sin7A
D = cosA - cos3A - cos5A + cos7A
Therefore we want to show that N/D = cot2A.
We shall use these identities:
sin x - sin y = 2cos((x+y)/2)*sin((x-y)/2)
cos x - cos y = -2sin((x+y)/2)*sin((x-y)2)
N = -(sin7A - sinA) + sin5A - sin3A
= -2cos4A*sin3A + 2cos4A*sinA
= 2cos4A(sinA - sin3A)
= 2cos4A*2cos(2A)sin(-A)
= -4cos4A*cos2A*sinA
D = cos7A + cosA - (cos5A + cos3A)
= 2cos4A*cos3A - 2cos4A*cosA
= 2cos4A(cos3A - cosA)
= 2cos4A*(-2)sin2A*sinA
= -4cos4A*sin2A*sinA
Therefore
N/D = [-4cos4A*cos2A*sinA]/[-4cos4A*sin2A*sinA]
= cos2A/sin2A
= cot2A
This verifies the identity.
That is where the line crosses the x axis or where y=0
set y=0
Bx=A
find x value
divie both sides by B
x=A/B
the x intercept is x=A/B
Answer:
The missing reason in the proof is transitive property
Step-by-step explanation:
<u>Statement </u> <u>Reason </u>
1. x ∥ y w is a transversal 1. given
2. ∠2 ≅ ∠3 2. def. of vert. ∠s
3. ∠2 ≅ ∠6 3. def. of corr. ∠s
4. ∠3 ≅ ∠6 4. ??????????
From the statements 2 and 3
The previous proved statement to make use of the transitive property reason or proof
∴ 4. ∠3 ≅ ∠6 4. transitive property
Note: the transitive property states that: If a = b and b = c, then a = c.
Answer:
* Elimination; a coefficient in Equation I is an integer multiple of a coefficient in Equation II.
* Elimination; a coefficient in Equation II is an integer multiple of a coefficient in Equation I.
Step-by-step explanation:
Equation I: 4x − 5y = 4
Equation II: 2x + 3y = 2
These equation can only be solved by Elimination method
Where to Eliminate x :
We Multiply Equation I by a coefficient of x in Equation II and Equation II by the coefficient of x in Equation I
Hence:
Equation I: 4x − 5y = 4 × 2
Equation II: 2x + 3y = 2 × 4
8x - 10y = 20
8x +12y = 6
Therefore, the valid reason using the given solution method to solve the system of equations shown is:
* Elimination; a coefficient in Equation I is an integer multiple of a coefficient in Equation II.
* Elimination; a coefficient in Equation II is an integer multiple of a coefficient in Equation I.