What is the general solution for 2cos^2(x)+3cos(x)=4cos(x)+1 ?

The general solution for 2cos^2(x)+3cos(x)=4cos(x)+1 is x=2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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2cos^2(x)+3cos(x)=4cos(x)+1

2 cos^{2} (x) + 3 cos (x) = 4 cos (x) + 1

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

Solution steps

2 cos^{2} (x) + 3 cos (x) = 4 cos (x) + 1

Solve by substitution

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

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

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

6 sin^{2} (x) + 5 sin (x) = 0

sin (x) = - \frac{1}{2}, (0, 2 π)

tan (θ) = \frac{4}{3}, cos (θ) < 0

cot (x) = \frac{sin ( x )}{cos ( x )}

0.6 = \frac{cosh ( 0.2 m )}{cosh ( 0.4 m )}

What is the general solution for 2cos^2(x)+3cos(x)=4cos(x)+1 ?
The general solution for 2cos^2(x)+3cos(x)=4cos(x)+1 is x=2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin