What is the general solution for 4cos^2(x)-6=5cos(x) ?

The general solution for 4cos^2(x)-6=5cos(x) is x=2.41885…+2pin,x=-2.41885…+2pin

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4cos^2(x)-6=5cos(x)

4 cos^{2} (x) - 6 = 5 cos (x)

x = 2.41885 \dots + 2 πn, x = - 2.41885 \dots + 2 πn

Solution steps

4 cos^{2} (x) - 6 = 5 cos (x)

Solve by substitution

cos (x) = 2, cos (x) = - \frac{3}{4}

cos (x) = 2 :

No Solution

cos (x) = - \frac{3}{4} : x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

Combine all the solutions

x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

Show solutions in decimal form

x = 2.41885 \dots + 2 πn, x = - 2.41885 \dots + 2 πn

tan (θ) = \frac{- 3}{2}

7 sin (x + 5) = 1

2 sin (x) tan (2 x) - 3 tan (2 x) = 0

tan (x) = \frac{12}{8}

cos (2 t) - cos (t) = - 0.5, 0 \leq t \leq 2 π

What is the general solution for 4cos^2(x)-6=5cos(x) ?
The general solution for 4cos^2(x)-6=5cos(x) is x=2.41885…+2pin,x=-2.41885…+2pin