Answer: cos(x)
Step-by-step explanation:
We have
sin ( x + y ) = sin(x)*cos(y) + cos(x)*sin(y) (1) and
cos ( x + y ) = cos(x)*cos(y) - sin(x)*sin(y) (2)
From eq. (1)
if x = y
sin ( x + x ) = sin(x)*cos(x) + cos(x)*sin(x) ⇒ sin(2x) = 2sin(x)cos(x)
From eq. 2
If x = y
cos ( x + x ) = cos(x)*cos(x) - sin(x)*sin(x) ⇒ cos²(x) - sin²(x)
cos (2x) = cos²(x) - sin²(x)
Hence:The expression:
cos(2x) cos(x) + sin(2x) sin(x) (3)
Subtition of sin(2x) and cos(2x) in eq. 3
[cos²(x)-sin²(x)]*cos(x) + [(2sen(x)cos(x)]*sin(x)
and operating
cos³(x) - sin²(x)cos(x) + 2sin²(x)cos(x) = cos³(x) + sin²(x)cos(x)
cos (x) [ cos²(x) + sin²(x) ] = cos(x)
since cos²(x) + sin²(x) = 1
285 liters is 75.289 U.S. gallons.
Answer: the solutions to the system of equations are x = 2 and x = 1
Step-by-step explanation:
The system of equations given equation is
y = 3x - 2 - - - - - - - - - - 1
y = x^2 - - - - - - - - - - - - 2
Substituting 1 into equation 2, it becomes
x^2 = 3x - 2
x^2 - 3x + 2 = 0
We would apply the method of factorization in solving the equation. We will get two numbers such that when added, the result would be - 3x and when multiplied, the result would be 2x^2. The numbers are - 2x and - x. It becomes
x^2 - 2x - x + 2 = 0
x(x - 2) - 1(x - 2) = 0
(x - 2)(x - 1) = 0
x - 2 = 0 or x - 1 = 0
x = 2 or x = 1
.
The equivalent expression for (x + 4)^5 is 
The expression is given as:
To expand the expression, we make use of Pascal triangle, where:
5:= 1 5 10 10 5 1
So, we have:
Evaluate the exponents
Evaluate the products
Hence, the equivalent expression for (x + 4)^5 is
Read more about binomial expressions at:
brainly.com/question/13602562
Answer:
A. NO
B. YES
C: YES
D: NO
Step-by-step explanation:
