What is the general solution for 2cos(x)=cos(2x) ?

The general solution for 2cos(x)=cos(2x) is x=1.94553…+2pin,x=-1.94553…+2pin

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2cos(x)=cos(2x)

2 cos (x) = cos (2 x)

x = 1.94553 \dots + 2 πn, x = - 1.94553 \dots + 2 πn

Solution steps

2 cos (x) = cos (2 x)

Subtract

cos (2 x)

from both sides

2 cos (x) - cos (2 x) = 0

Rewrite using trig identities

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

Solve by substitution

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

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

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

No Solution

Combine all the solutions

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

Show solutions in decimal form

x = 1.94553 \dots + 2 πn, x = - 1.94553 \dots + 2 πn

3 cos^{2} (θ) + cos (θ) = 0

cos^{2} (θ) = 0.75

cos (y_{0}) = \frac{( a _{0} \cdot n _{0} )}{∣} a_{0} ∣

tan (θ) = - 6

8 sin (x) tan (x) - 7 tan (x) = 0

What is the general solution for 2cos(x)=cos(2x) ?
The general solution for 2cos(x)=cos(2x) is x=1.94553…+2pin,x=-1.94553…+2pin