Recall that
cos²(<em>x</em>) + sin²(<em>x</em>) = 1
Then in the equation
1 - cos(<em>x</em>) = 2 - 2 sin²(<em>x</em>)
we can rewrite as
1 - cos(<em>x</em>) = 2 (1 - sin²(<em>x</em>))
1 - cos(<em>x</em>) = 2 cos²(<em>x</em>)
2 cos²(<em>x</em>) + cos(<em>x</em>) - 1 = 0
Factorize the left side as
(2 cos(<em>x</em>) - 1) (cos(<em>x</em>) + 1) = 0
so that
2 cos(<em>x</em>) - 1 = 0 <u>or</u> cos(<em>x</em>) + 1 = 0
cos(<em>x</em>) = 1/2 <u>or</u> cos(<em>x</em>) = -1
On the interval (-<em>π</em>, <em>π</em>) (note that this interval is open, so we don't allow <em>x</em> = <em>π</em>), we have
• cos(<em>x</em>) = 1/2 for <em>x</em> = <em>π</em>/3 and <em>x</em> = -<em>π</em>/3
• cos(<em>x</em>) = -1 for <em>x</em> = <em>π</em>
Answer:
37.50
Step-by-step explanation:
2/5x + 15 = 30
2/5x = 15
x = 15 ( 5/2)
x = 37.50
Answer is 91.56 You add all the numbers up and divide by 9(There are 9 numbers in the sequence).
Answer:
x=4
Step-by-step explanation:
5x+10=30
Subtract 10 from each side
5x=20
Divided each side by 5
x=4
Answer:
(x+4)(x+6)
Step-by-step explanation:
First we factorise:
x²+4x+6x+24
x(x+4)+6(x+4)
(x+4)(x+6)
So the last one is equivalent
