What is the general solution for cos(2x)=-1/(sqrt(2)) ?

The general solution for cos(2x)=-1/(sqrt(2)) is x=(3pi)/8+pin,x=(5pi)/8+pin

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cos(2x)=-1/(sqrt(2))

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

x = \frac{3 π}{8} + πn, x = \frac{5 π}{8} + πn

Solution steps

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

Simplify

- \frac{1}{2} : - \frac{2}{2}

General solutions for

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

2 x = \frac{3 π}{4} + 2 πn, 2 x = \frac{5 π}{4} + 2 πn

Solve

2 x = \frac{3 π}{4} + 2 πn : x = \frac{3 π}{8} + πn

Solve

2 x = \frac{5 π}{4} + 2 πn : x = \frac{5 π}{8} + πn

x = \frac{3 π}{8} + πn, x = \frac{5 π}{8} + πn

2 sec^{2} (x) + 5 sec (x) + 2 = 0

sin^{2} (θ) = 8 (cos (- θ) + 1)

tan (x) = \frac{7.1}{5}

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

sin (2 θ) = - \frac{1}{2}, θ \geq 0

What is the general solution for cos(2x)=-1/(sqrt(2)) ?
The general solution for cos(2x)=-1/(sqrt(2)) is x=(3pi)/8+pin,x=(5pi)/8+pin