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

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

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2cos(x)-1=sec(x)

2 cos (x) - 1 = sec (x)

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = 2 πn

Solution steps

2 cos (x) - 1 = sec (x)

Subtract

sec (x)

from both sides

2 cos (x) - 1 - sec (x) = 0

Rewrite using trig identities

- 1 + \frac{2}{sec ( x )} - sec (x) = 0

Solve by substitution

sec (x) = - 2, sec (x) = 1

sec (x) = - 2 : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

sec (x) = 1 : x = 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = 2 πn

2 - cos (x) = 2 + sin (x)

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

112 = 72 + 40 cos (18 t)

1 + sin (x) = (2) (cos (x))

cos (2 x) = - 0.32

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