cos (2x) = cos x
2 cos^2 x -1 = cos x using the double angle formula
2 cos ^2 x -cos x -1 =0
factor
(2 cos x+1) ( cos x -1) = 0
using the zero product property
2 cos x+1 =0 cos x -1 =0
2 cos x = -1 cos x =1
cos x = -1/2 cos x=1
taking the arccos of each side
arccos cos x = arccos (-1/2) arccos cos x = arccos 1
x = 120 degrees x=-120 degrees x=0
remember you get 2 values ( 2nd and 3rd quadrant)
these are the principal values
now we need to add 360
x = 120+ 360n x=-120+ 360n x = 0 + 360n where n is an integer
Answer:
Step-by-step explanation:
ur mom (94)
stock in a start-up company
The answer is 2/10
your just reducing the ratio
Answer:
I need the expressions
Step-by-step explanation:
(I don't have the experresions but I think it might be helpful to simplify)
- f - 5 ( 2 f - 3)
−f−10f+15
−f−(10f−15)
(−f−10f)+15
<u>−11f+15
</u>
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<u>Hope this helped</u>
