What is the general solution for 4cos^2(x)-2cos(x)-3=0 ?

The general solution for 4cos^2(x)-2cos(x)-3=0 is x=2.28020…+2pin,x=-2.28020…+2pin

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4cos^2(x)-2cos(x)-3=0

4 cos^{2} (x) - 2 cos (x) - 3 = 0

x = 2.28020 \dots + 2 πn, x = - 2.28020 \dots + 2 πn

Solution steps

4 cos^{2} (x) - 2 cos (x) - 3 = 0

Solve by substitution

cos (x) = \frac{1 + 13}{4}, cos (x) = \frac{1 - 13}{4}

cos (x) = \frac{1 + 13}{4} :

No Solution

cos (x) = \frac{1 - 13}{4} : x = arccos (\frac{1 - 13}{4}) + 2 πn, x = - arccos (\frac{1 - 13}{4}) + 2 πn

Combine all the solutions

x = arccos (\frac{1 - 13}{4}) + 2 πn, x = - arccos (\frac{1 - 13}{4}) + 2 πn

Show solutions in decimal form

x = 2.28020 \dots + 2 πn, x = - 2.28020 \dots + 2 πn

3 cos (x) = \frac{6}{π}

6 cos (2 θ) = 18 cos (θ) - 12

cos (\frac{2}{3} x - \frac{π}{2}) = 1

tan^{2} (x) sin (x) = sin (x), 0 \leq x \leq 2 π

- 3 sin (t) = 0

What is the general solution for 4cos^2(x)-2cos(x)-3=0 ?
The general solution for 4cos^2(x)-2cos(x)-3=0 is x=2.28020…+2pin,x=-2.28020…+2pin