What is the general solution for 2cos^3(x)-1=0 ?

The general solution for 2cos^3(x)-1=0 is x=0.65392…+2pin,x=2pi-0.65392…+2pin

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2cos^3(x)-1=0

2 cos^{3} (x) - 1 = 0

x = 0.65392 \dots + 2 πn, x = 2 π - 0.65392 \dots + 2 πn

Solution steps

2 cos^{3} (x) - 1 = 0

Solve by substitution

cos (x) = - \frac{2 ^{\frac{2}{3}}}{4} + i \frac{2 ^{\frac{2}{3}} 3}{4} :

No Solution

cos (x) = - \frac{2 ^{\frac{2}{3}}}{4} - i \frac{2 ^{\frac{2}{3}} 3}{4} :

No Solution

Combine all the solutions

Show solutions in decimal form

x = 0.65392 \dots + 2 πn, x = 2 π - 0.65392 \dots + 2 πn

\frac{1 - tan ^{2} ( θ )}{1 + tan ^{2} ( θ )} = 2 cos^{2} (- 1)

sin (x) = - \frac{5}{6}

5 cot (x) + 3 = 8

cos (x) = - \frac{3}{2}, 0 \leq x \leq 2 π

9 sin (θ) + 2 = 0

What is the general solution for 2cos^3(x)-1=0 ?
The general solution for 2cos^3(x)-1=0 is x=0.65392…+2pin,x=2pi-0.65392…+2pin