Trigonometry Examples

Solve for x cos(6y)=cos(3y)^2-sin(3y)^2
Step 1
Simplify .
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Step 1.1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 1.2
Expand using the FOIL Method.
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Step 1.2.1
Apply the distributive property.
Step 1.2.2
Apply the distributive property.
Step 1.2.3
Apply the distributive property.
Step 1.3
Simplify terms.
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Step 1.3.1
Combine the opposite terms in .
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Step 1.3.1.1
Reorder the factors in the terms and .
Step 1.3.1.2
Add and .
Step 1.3.1.3
Add and .
Step 1.3.2
Simplify each term.
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Step 1.3.2.1
Multiply .
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Step 1.3.2.1.1
Raise to the power of .
Step 1.3.2.1.2
Raise to the power of .
Step 1.3.2.1.3
Use the power rule to combine exponents.
Step 1.3.2.1.4
Add and .
Step 1.3.2.2
Rewrite using the commutative property of multiplication.
Step 1.3.2.3
Multiply .
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Step 1.3.2.3.1
Raise to the power of .
Step 1.3.2.3.2
Raise to the power of .
Step 1.3.2.3.3
Use the power rule to combine exponents.
Step 1.3.2.3.4
Add and .
Step 1.4
Apply the cosine double-angle identity.
Step 1.5
Multiply by .
Step 2
For the two functions to be equal, the arguments of each must be equal.
Step 3
Move all terms containing to the left side of the equation.
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Step 3.1
Subtract from both sides of the equation.
Step 3.2
Subtract from .
Step 4
Since , the equation will always be true for any value of .
All real numbers
Step 5
The result can be shown in multiple forms.
All real numbers
Interval Notation: