What is the general solution for 2cos(x)-9=-4sec(x) ?

The general solution for 2cos(x)-9=-4sec(x) is x= pi/3+2pin,x=(5pi)/3+2pin

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2cos(x)-9=-4sec(x)

2 cos (x) - 9 = - 4 sec (x)

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

Solution steps

2 cos (x) - 9 = - 4 sec (x)

Subtract

- 4 sec (x)

from both sides

2 cos (x) - 9 + 4 sec (x) = 0

Rewrite using trig identities

- 9 + \frac{2}{sec ( x )} + 4 sec (x) = 0

Solve by substitution

sec (x) = 2, sec (x) = \frac{1}{4}

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

sec (x) = \frac{1}{4} :

No Solution

Combine all the solutions

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

2 sin (θ) + 4 = 4

4 sin^{2} (x) + (23 + 2) sin (x) + 3 = 0

- cos (x) - 2 cos^{2} (x) = 0

3 csc (x) = 2 csc (x) + 2

sec (x) = tan (x) + cot (x)

What is the general solution for 2cos(x)-9=-4sec(x) ?
The general solution for 2cos(x)-9=-4sec(x) is x= pi/3+2pin,x=(5pi)/3+2pin