What is the general solution for cos(x)= 1/3 ,cos(2x) ?

The general solution for cos(x)= 1/3 ,cos(2x) is No Solution for x\in\mathbb{R}

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cos(x)= 1/3 ,cos(2x)

cos (x) = \frac{1}{3}, cos (2 x)

No Solution for x \in R

Solution steps

cos (x) = \frac{1}{3}, cos (2 x)

Apply trig inverse properties

cos (x) = \frac{1}{3}

General solutions for

cos (x) = \frac{1}{3}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

Solutions for the range

cos (2 x)

No Solution for x \in R

3 sin (2 x) \cdot cos (x) = 2 sin^{3} (x)

x, sin (x) \cdot cos (y) = 0

2 cos (3 x - 1) = - 1

\frac{0.866}{sin ( x )} = 1.53

3 sin (2 x) + 1 = 2

What is the general solution for cos(x)= 1/3 ,cos(2x) ?
The general solution for cos(x)= 1/3 ,cos(2x) is No Solution for x\in\mathbb{R}