Trigonometry Examples

Solve for x cos(x)^4-sin(x)^4=cos(2x)
Step 1
Simplify the left side.
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Step 1.1
Simplify .
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Step 1.1.1
Simplify the expression.
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Step 1.1.1.1
Rewrite as .
Step 1.1.1.2
Rewrite as .
Step 1.1.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 1.1.3
Rearrange terms.
Step 1.1.4
Apply pythagorean identity.
Step 1.1.5
Multiply by .
Step 1.1.6
Apply the cosine double-angle identity.
Step 2
Move all terms containing to the left side of the equation.
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Step 2.1
Subtract from both sides of the equation.
Step 2.2
Subtract from .
Step 3
Since , the equation will always be true for any value of .
All real numbers
Step 4
The result can be shown in multiple forms.
All real numbers
Interval Notation: