What is the general solution for cos(x)a= pi/3 ?

The general solution for cos(x)a= pi/3 is x=arccos(pi/(3a))+2pin,x=-arccos(pi/(3a))+2pin

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cos(x)a= pi/3

cos (x) a = \frac{π}{3}

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

Solution steps

cos (x) a = \frac{π}{3}

Divide both sides by

a; a \neq = 0

cos (x) a = \frac{π}{3}

Divide both sides by

a; a \neq = 0

\frac{cos ( x ) a}{a} = \frac{\frac{π}{3}}{a}; a \neq = 0

Simplify

\frac{cos ( x ) a}{a} = \frac{\frac{π}{3}}{a}

Simplify

\frac{cos ( x ) a}{a} : cos (x)

\frac{cos ( x ) a}{a}

Cancel the common factor:

a

= cos (x)

Simplify

\frac{\frac{π}{3}}{a} : \frac{π}{3 a}

\frac{\frac{π}{3}}{a}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{3 a}

cos (x) = \frac{π}{3 a}; a \neq = 0

cos (x) = \frac{π}{3 a}; a \neq = 0

cos (x) = \frac{π}{3 a}; a \neq = 0

Apply trig inverse properties

cos (x) = \frac{π}{3 a}

General solutions for

cos (x) = \frac{π}{3 a}

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

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

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

cos^{2} (x) = - \frac{1}{4}

2 sin^{2} (x) - cos (x) - 2 = 0

2 sin (4 x) + (3) = 0

3 = sin (2 x)

6 cos (2 θ) + 3 = 4 cos (2 θ) + 4

What is the general solution for cos(x)a= pi/3 ?
The general solution for cos(x)a= pi/3 is x=arccos(pi/(3a))+2pin,x=-arccos(pi/(3a))+2pin