What is the general solution for 4cos^2(x)-4=15cos(x) ?

The general solution for 4cos^2(x)-4=15cos(x) is x=1.82347…+2pin,x=-1.82347…+2pin

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4cos^2(x)-4=15cos(x)

4 cos^{2} (x) - 4 = 15 cos (x)

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

Solution steps

4 cos^{2} (x) - 4 = 15 cos (x)

Solve by substitution

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

cos (x) = 4 :

No Solution

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

Combine all the solutions

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

Show solutions in decimal form

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

(cos (θ) - 1) sin (θ) = 0

sin (a) = 0

6 cot (θ) - 5 = 0

8 cos (x) - 8 sin (x) = 0

sin (4 x) cos (x) - sin (x) cos (4 x) = \frac{1}{2}

What is the general solution for 4cos^2(x)-4=15cos(x) ?
The general solution for 4cos^2(x)-4=15cos(x) is x=1.82347…+2pin,x=-1.82347…+2pin