What is the general solution for -2cos(x)+1=5cos(x)+0 ?

The general solution for -2cos(x)+1=5cos(x)+0 is x=1.42744…+2pin,x=2pi-1.42744…+2pin

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-2cos(x)+1=5cos(x)+0

- 2 cos (x) + 1 = 5 cos (x) + 0

x = 1.42744 \dots + 2 πn, x = 2 π - 1.42744 \dots + 2 πn

Solution steps

- 2 cos (x) + 1 = 5 cos (x) + 0

Solve by substitution

cos (x) = \frac{1}{7}

cos (x) = \frac{1}{7} : x = arccos (\frac{1}{7}) + 2 πn, x = 2 π - arccos (\frac{1}{7}) + 2 πn

Combine all the solutions

x = arccos (\frac{1}{7}) + 2 πn, x = 2 π - arccos (\frac{1}{7}) + 2 πn

Show solutions in decimal form

x = 1.42744 \dots + 2 πn, x = 2 π - 1.42744 \dots + 2 πn

sin (x) = - 0.45

sin (x) = - 0.59

sin (x) = - 0.55

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

cot (y) + 2 = 1 - csc (y)

What is the general solution for -2cos(x)+1=5cos(x)+0 ?
The general solution for -2cos(x)+1=5cos(x)+0 is x=1.42744…+2pin,x=2pi-1.42744…+2pin