Answer:
Step-by-step explanation:
given the expression;
cos(2x) = cos(x)
According to trig identity;
cos(2x) = cos(x+x)
cos(2x) = cos x cos x - sinx sinx
cos(2x) = cos²(x)-sin²(x)
cos(2x) = cos²(x)-(1-cos²x)
cos(2x) = cos²(x)+cos²x-1
cos(2x) = 2cos²(x)-1
2cos²(x)-1 = cos(x)
let P = cosx
2P²-1 = P
2P²-P-1 = 0
Factorize;
2P²-2P+P-1 = 0
2P(P-1)+1(P-1) = 0
2P - 1 = 0 and P-1 = 0
P = 1/2 and 1
cosx = 1/2 and cos x = 1
x = arccos 1/2
x = π/3
Also;
x = arccos1
x = 0
Hence the value of x are 0 and π/3
Also the angle = π+ π/3 = 4π/3
The angles are 0, π/3 and 4π/3
An octagon has 8 sides. Each side is given as 2a + 1
Perimeter = 8(2a + 1)
= 16a + 8
Answer: 16a + 8
Answer:
Step-by-step explanation:
We are asked to find the measure of each exterior angle of a regular dodecagon.
We know that a regular dodecagon is a 12 sided regular polygon with each side equal.
We know that measure of each angle of n-sided regular polygon can be found using formula:
Upon substituting 
in above formula, we will get:
Therefore, the measure of each exterior angle of a regular dodecagon is 30 degrees.
Answer:
i) True
ii) True
Step-by-step explanation:
<u>Given :-</u>
Point (-1, 2)
<u>To Find :</u>
Whether the point is a solution of :
- y = -2x
- y = x + 3
<u>Solving :-</u>
Substitute the value of the point in each of the equations.
=> y = -2x
=> 2 = -2(-1)
=> 2 = 2 [∴ The point makes it true]
=> y = x + 3
=> 2 = -1 + 3
=> 2 = 2 [∴ The point makes it true]
Answer:
Step-by-step explanation:
Let f(x) = 3x² - x³ - 3x + 5 and g(x) = x - 1 - x²
-x² + x - 1) -x³ + 3x² - 3x + 5(x - 2
-x³ + x² - x
-------------------------
2x² - 2x + 5
2x² - 2x + 2
----------------------
3
