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emmasim [6.3K]
3 years ago
14

4cos^2(x)-7cos(x)+3 Please help and explain how you did it :)

Mathematics
1 answer:
dangina [55]3 years ago
7 0

I assume you're asked to solve

4 cos²(<em>x</em>) - 7 cos(<em>x</em>) + 3 = 0

Factor the left side:

(4 cos(<em>x</em>) - 3) (cos(<em>x</em>) - 1) = 0

Then either

4 cos(<em>x</em>) - 3 = 0   <u>or</u>   cos(<em>x</em>) - 1 = 0

cos(<em>x</em>) = 3/4   <u>or</u>   cos(<em>x</em>) = 1

From the first case, we get

<em>x</em> = cos⁻¹(3/4) + 2<em>nπ</em>  <u>or</u>   <em>x</em> = -cos⁻¹(3/4) + 2<em>nπ</em>

and from the second,

<em>x</em> = <em>nπ</em>

where <em>n</em> is any integer.

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