What is the general solution for 16cos(2x)-4=0 ?

The general solution for 16cos(2x)-4=0 is x=(1.31811…)/2+pin,x=pi-(1.31811…)/2+pin

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16cos(2x)-4=0

16 cos (2 x) - 4 = 0

x = \frac{1.31811 \dots}{2} + πn, x = π - \frac{1.31811 \dots}{2} + πn

Solution steps

16 cos (2 x) - 4 = 0

Move

4

to the right side

16 cos (2 x) = 4

Divide both sides by

16

cos (2 x) = \frac{1}{4}

Apply trig inverse properties

2 x = arccos (\frac{1}{4}) + 2 πn, 2 x = 2 π - arccos (\frac{1}{4}) + 2 πn

Solve

2 x = arccos (\frac{1}{4}) + 2 πn : x = \frac{arccos ( \frac{1}{4} )}{2} + πn

Solve

2 x = 2 π - arccos (\frac{1}{4}) + 2 πn : x = π - \frac{arccos ( \frac{1}{4} )}{2} + πn

x = \frac{arccos ( \frac{1}{4} )}{2} + πn, x = π - \frac{arccos ( \frac{1}{4} )}{2} + πn

Show solutions in decimal form

x = \frac{1.31811 \dots}{2} + πn, x = π - \frac{1.31811 \dots}{2} + πn

- csc (x) cot (x) = 0

4 sin (θ) = \frac{1}{cos ( θ )}

3 sin (2 x) = - sin (x)

10 sin (A) + 16 = 3 sin (A) + 9

y, x = cos (y)

What is the general solution for 16cos(2x)-4=0 ?
The general solution for 16cos(2x)-4=0 is x=(1.31811…)/2+pin,x=pi-(1.31811…)/2+pin