What is the general solution for 4cos^2(x)-4sqrt(2)cos(x)+2=0 ?

The general solution for 4cos^2(x)-4sqrt(2)cos(x)+2=0 is x= pi/4+2pin,x=(7pi)/4+2pin

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4cos^2(x)-4sqrt(2)cos(x)+2=0

4 cos^{2} (x) - 42 cos (x) + 2 = 0

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Solution steps

4 cos^{2} (x) - 42 cos (x) + 2 = 0

Solve by substitution

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

cos (x) = \frac{2}{2} : x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Combine all the solutions

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

sin (\frac{2 π}{3} - x) + sin (\frac{2 π}{3} + x) = 0

sin (θ) cos (θ) = cot (θ)

cot (θ) = - \frac{4}{3}

tan (x) = \frac{6}{10}

tan (A) = 34

What is the general solution for 4cos^2(x)-4sqrt(2)cos(x)+2=0 ?
The general solution for 4cos^2(x)-4sqrt(2)cos(x)+2=0 is x= pi/4+2pin,x=(7pi)/4+2pin