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

The general solution for 2cos(x)+1=sec(x) is x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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

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

x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 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) = - 1, sec (x) = 2

sec (x) = - 1 : x = π + 2 πn

sec (x) = 2 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

2 sin (θ) = 1, 0 \leq θ \leq 2 π

sin (8 θ) - sin (6 θ) = cos (7 θ), 0 \leq θ \leq 2 π

cos (2 x) + 14 sin^{2} (x) = 10

6 tan (b) + 14 = 0

0 = - 2 cos (x)

What is the general solution for 2cos(x)+1=sec(x) ?
The general solution for 2cos(x)+1=sec(x) is x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin