What is the general solution for -8cos(x)=-6sec(x)+8 ?

The general solution for -8cos(x)=-6sec(x)+8 is x= pi/3+2pin,x=(5pi)/3+2pin

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-8cos(x)=-6sec(x)+8

- 8 cos (x) = - 6 sec (x) + 8

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

Solution steps

- 8 cos (x) = - 6 sec (x) + 8

Subtract

- 6 sec (x) + 8

from both sides

- 8 cos (x) + 6 sec (x) - 8 = 0

Rewrite using trig identities

- 8 - \frac{8}{sec ( x )} + 6 sec (x) = 0

Solve by substitution

sec (x) = 2, sec (x) = - \frac{2}{3}

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

sec (x) = - \frac{2}{3} :

No Solution

Combine all the solutions

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

cos (2 θ) + sin (θ) = 1

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

4 cos (x) - 1 = 0

sin (2 θ) = - \frac{1}{2}, 0 \leq θ < 2 π

sin (θ) = 1 - sin (θ)

What is the general solution for -8cos(x)=-6sec(x)+8 ?
The general solution for -8cos(x)=-6sec(x)+8 is x= pi/3+2pin,x=(5pi)/3+2pin