What is the general solution for 4cos(2x)=1-3cos(x) ?

The general solution for 4cos(2x)=1-3cos(x) is x=0.89566…+2pin,x=2pi-0.89566…+2pin,x=pi+2pin

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4cos(2x)=1-3cos(x)

4 cos (2 x) = 1 - 3 cos (x)

x = 0.89566 \dots + 2 πn, x = 2 π - 0.89566 \dots + 2 πn, x = π + 2 πn

Solution steps

4 cos (2 x) = 1 - 3 cos (x)

Subtract

1 - 3 cos (x)

from both sides

4 cos (2 x) - 1 + 3 cos (x) = 0

Rewrite using trig identities

- 5 + 3 cos (x) + 8 cos^{2} (x) = 0

Solve by substitution

cos (x) = \frac{5}{8}, cos (x) = - 1

cos (x) = \frac{5}{8} : x = arccos (\frac{5}{8}) + 2 πn, x = 2 π - arccos (\frac{5}{8}) + 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = arccos (\frac{5}{8}) + 2 πn, x = 2 π - arccos (\frac{5}{8}) + 2 πn, x = π + 2 πn

Show solutions in decimal form

x = 0.89566 \dots + 2 πn, x = 2 π - 0.89566 \dots + 2 πn, x = π + 2 πn

0 = 32 π sec (x^{2}) tan (x)

1 \cdot sin (54.8 6^{\circ}) = 2.451 \cdot sin (x)

\frac{cot ( θ )}{csc ( θ )} = sin (θ)

cos (t) = - \frac{2}{3}

sin (θ) = 1 + (1 - (cos (θ) - 1)^{2})

What is the general solution for 4cos(2x)=1-3cos(x) ?
The general solution for 4cos(2x)=1-3cos(x) is x=0.89566…+2pin,x=2pi-0.89566…+2pin,x=pi+2pin