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2cos2x=1

or, cos2x = 1/2 = cos pi/3 or cos5pi/3

so, 2x =pi/3 or 5pi/3

so, x = pi/6 or 5pi/6

2cos2x = 1

=> cos2x = 1/2

=> 2x = arc cos 1/2

=> 2x = pi/3 or 60 deg

=> x = pi/3/2 = pi/6 radians or 60/2 = 30 deg

If you don't know what is arc (trig ratio)?, read on below...

if sin(x) = y,

x = arc sin y

It basically asks you for what angle does the trig. ratio= y

Hope this helps...

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sin2x + sin4x = 0 sin2x + 2sin2xcos2x = 0 sin2x(a million + 2cos2x) = 0 sin2x = 0 or cos2x = -a million/2 sin2x = 0 ==> 2x = ok? ==> x = ok?/2 cos2x = -a million/2 ==> 2x = ±2?/3 + ok.2? ==> x = ±?/3 + ok? The suggestions indoors the section [0,2?) are 0, ?/2, ?, 3?/2, ?/3, 4?/3, 2?/3, 5?/3

Given:

2*cos(2*x) = 1

Isolate cosine:

cos(2*x) = 1/2

Take arccosine:

2*x = arccos(1/2)

Divide by 2:

x = arccos(1/2)/2

Crunch numbers:

x = 30 deg

Do you mean 2 cos(2x) = 1 or 2 cos^2(x) = 1???

First case:

2 cos(2x) = 1

cos(2x) = 1/2

Now we need to find all angles in circle where cos = 1/2

If you wish to find all values of x on interval [0, 360) or [0, 2π), then you need to find all values of 2x on interval [0, 720) or [0, 4π)

cos(2x) = 1/2

2x = 60, 300, 420, 660 . . . . . or . . . . . 2x = π/3, 5π/3, 7π/3, 11π/3

x = 30, 150, 210, 330 . . . . . . or . . . . . x = π/6, 5π/6, 7π/6, 11π/6

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Second case

2 cos^2(x) = 1

cos^2(x) = 1/2

cos(x) = ± 1/√2

x = 45, 135, 225, 315 . . . . or . . . . x = π/4, 3π/4, 5π/4, 7π/4

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cos2x = 1/2

2x = 60

x = 30 (or

...Or if you meant 2cos^2(x) = 1

cos^2(x) = 1/2

xos(x) = +/- 1/√2 = 45

2cos(2x) = 1

cos(2x) = 1/2

1 + cos^2(x) = 1/2

cos^2(x) = -1/2

cos(x) = ±√(2)/2*i