What is the general solution for 2cos(x)-7=4sec(x) ?

The general solution for 2cos(x)-7=4sec(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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2cos(x)-7=4sec(x)

2 cos (x) - 7 = 4 sec (x)

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

Solution steps

2 cos (x) - 7 = 4 sec (x)

Subtract

4 sec (x)

from both sides

2 cos (x) - 7 - 4 sec (x) = 0

Rewrite using trig identities

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

Solve by substitution

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

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

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

No Solution

Combine all the solutions

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

3 (cos (2 x) + \frac{3}{2}) = 6

sin^{2} (x) - 3 = 2 sin (x)

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

6 cos (θ) = 3

4 cos^{3} (x) = cos (x)

What is the general solution for 2cos(x)-7=4sec(x) ?
The general solution for 2cos(x)-7=4sec(x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin