What is the general solution for 4cos^2(x)-5cos(x)-6=0 ?

The general solution for 4cos^2(x)-5cos(x)-6=0 is x=2.41885…+2pin,x=-2.41885…+2pin

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4cos^2(x)-5cos(x)-6=0

4 cos^{2} (x) - 5 cos (x) - 6 = 0

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

Solution steps

4 cos^{2} (x) - 5 cos (x) - 6 = 0

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

3 sec^{2} (\frac{x}{2}) - 4 sec (\frac{x}{2}) - 4 = 0

tan (x) = \frac{3}{10 cos ( x )}, 0^{\circ} < x < 9 0^{\circ}

2 cos^{2} (x) - 3 cos (x) = 0, 0, 2 π

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

2 cos (2 θ) - 7 cos (θ) + 2 = - 4 cos (θ)

What is the general solution for 4cos^2(x)-5cos(x)-6=0 ?
The general solution for 4cos^2(x)-5cos(x)-6=0 is x=2.41885…+2pin,x=-2.41885…+2pin