What is the general solution for 2cos^2(x)-7cos(x)=-3 ?

The general solution for 2cos^2(x)-7cos(x)=-3 is x= pi/3+2pin,x=(5pi)/3+2pin

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2cos^2(x)-7cos(x)=-3

2 cos^{2} (x) - 7 cos (x) = - 3

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

Solution steps

2 cos^{2} (x) - 7 cos (x) = - 3

Solve by substitution

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

cos (x) = 3 :

No Solution

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

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

sin (x) + 2 sin (2 x) = 0

2 sin^{2} (x) - 1 = - sin (x)

cosh (x) cosh (1) - sinh (x) sinh (1) = 2

cos^{2} (x) = \frac{3 ( 1 - sin ( x ) )}{2}

2 cos (θ) = 2 cos (3 θ)

What is the general solution for 2cos^2(x)-7cos(x)=-3 ?
The general solution for 2cos^2(x)-7cos(x)=-3 is x= pi/3+2pin,x=(5pi)/3+2pin