What is the general solution for cos(2a)= 2/3 ,sin(a) ?

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

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cos(2a)= 2/3 ,sin(a)

cos (2 a) = \frac{2}{3}, sin (a)

No Solution for a \in R

Solution steps

cos (2 a) = \frac{2}{3}, sin (a)

Apply trig inverse properties

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

Solve

2 a = arccos (\frac{2}{3}) + 2 πn : a = \frac{arccos ( \frac{2}{3} )}{2} + πn

Solve

2 a = 2 π - arccos (\frac{2}{3}) + 2 πn : a = π - \frac{arccos ( \frac{2}{3} )}{2} + πn

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

Solutions for the range

sin (a)

No Solution for a \in R

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sin^{4} (x) + cos^{4} (x) = cos^{4} (x)

cot (x) = \frac{40}{32}

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