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

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

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

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

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

Solution steps

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

Subtract

1

from both sides

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

cos (x) tan (x) = 5 tan (x)

- 5 sin (5 x) = 0

16 cos^{2} (θ) = 12

cos (2 x) = 2 cos (x)

sin (θ) + 3 cos (θ) = 1

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