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tresset_1 [31]
2 years ago
12

Find all solutions to the equation. cos^2x + 2 cos x + 1 = 0

Mathematics
1 answer:
Black_prince [1.1K]2 years ago
3 0

Answer:

x = pi, 3pi, 5pi  etc

x = -pi, -3pi, -5pi etc

Step-by-step explanation:

cos^2 x + 2 cos x + 1 = 0

replace cos x with m

m^2 + 2m +1 = 0

solve by factoring  (this is a^2 +2ab+b^2 = (a+b)^2  where a =m and b=1)

(m+1)^2=0

take the square root of each side

m+1 =0

m=-1

now replace m with cos x

cos x = -1

take arccos  of each side

arccos cos x = arccos (-1)

x = pi, 3pi, 5pi  etc


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