What is the general solution for sqrt(2)cos(2x)+1=0 ?

The general solution for sqrt(2)cos(2x)+1=0 is x=(3pi)/8+pin,x=(5pi)/8+pin

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sqrt(2)cos(2x)+1=0

2 cos (2 x) + 1 = 0

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

Solution steps

2 cos (2 x) + 1 = 0

Move

1

to the right side

2 cos (2 x) = - 1

Divide both sides by

2

cos (2 x) = - \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

3 tan (x - 1) = 4, x \leq 2 π, 0

sin (x) = \frac{6 sin ( 2 0 ^{\circ} )}{4}

0 = 1.2209 \cdot cos (x) + 0.0422 \cdot cos (2 \cdot x)

5 sin (θ) + 3 = 0

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

What is the general solution for sqrt(2)cos(2x)+1=0 ?
The general solution for sqrt(2)cos(2x)+1=0 is x=(3pi)/8+pin,x=(5pi)/8+pin