What is the general solution for 3cos(x)+6=cos(x)+5 ?

The general solution for 3cos(x)+6=cos(x)+5 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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3cos(x)+6=cos(x)+5

3 cos (x) + 6 = cos (x) + 5

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

Solution steps

3 cos (x) + 6 = cos (x) + 5

Solve by substitution

cos (x) = - \frac{1}{2}

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

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

cos (x) = \frac{1}{3}, \frac{3 π}{2} < x < 2 π

\frac{2.68}{sin ( 12 6 ^{\circ} )} = \frac{1.2}{sin ( x )}

3 csc^{2} (x) - 5 csc (x) - 2 = 0

(cot (x) - 1) (3 tan (x) - 1) = 0

2 sin (x) cos (x) + cos (x) = 0, 0 \leq x \leq 2 π

What is the general solution for 3cos(x)+6=cos(x)+5 ?
The general solution for 3cos(x)+6=cos(x)+5 is x=(2pi)/3+2pin,x=(4pi)/3+2pin