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Identical expressions
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Similar expressions
- √2cos(2*x)-1=0
√2cos(2*x)+1=0 equation
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The solution
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____________ \/ 2*cos(2*x) + 1 = 0
$$\sqrt{2 \cos{\left(2 x \right)}} + 1 = 0$$
Detail solution
Given the equation
$$\sqrt{2 \cos{\left(2 x \right)}} + 1 = 0$$
transform
$$\sqrt{2} \sqrt{\cos{\left(2 x \right)}} + 1 = 0$$
$$\sqrt{2 \cos{\left(2 x \right)}} + 1 = 0$$
Do replacement
$$w = \cos{\left(2 x \right)}$$
Given the equation
$$\sqrt{2} \sqrt{w} + 1 = 0$$
Because equation degree is equal to = 1/2 and the free term = -1 < 0,
so the real solutions of the equation d'not exist
do backward replacement
$$\cos{\left(2 x \right)} = w$$
Given the equation
$$\cos{\left(2 x \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$2 x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
Or
$$2 x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$2 x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
substitute w:
$$\sqrt{2 \cos{\left(2 x \right)}} + 1 = 0$$
transform
$$\sqrt{2} \sqrt{\cos{\left(2 x \right)}} + 1 = 0$$
$$\sqrt{2 \cos{\left(2 x \right)}} + 1 = 0$$
Do replacement
$$w = \cos{\left(2 x \right)}$$
Given the equation
$$\sqrt{2} \sqrt{w} + 1 = 0$$
Because equation degree is equal to = 1/2 and the free term = -1 < 0,
so the real solutions of the equation d'not exist
do backward replacement
$$\cos{\left(2 x \right)} = w$$
Given the equation
$$\cos{\left(2 x \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$2 x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
Or
$$2 x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$2 x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
substitute w: