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

The general solution for 4(cos(x)+1)cos(x)=3 is x= pi/3+2pin,x=(5pi)/3+2pin

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

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

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

Solution steps

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

Solve by substitution

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

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

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

No Solution

Combine all the solutions

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

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

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

cos (2 a) = \frac{2}{3}, sin (a)

cot (2 x - 3) - 1 = 0

4 sin^{32} (x) - 3 cos^{2} (x) = 0

What is the general solution for 4(cos(x)+1)cos(x)=3 ?
The general solution for 4(cos(x)+1)cos(x)=3 is x= pi/3+2pin,x=(5pi)/3+2pin