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Trigonometry Examples
Step 1
Step 1.1
Use the product property of logarithms, .
Step 1.2
Expand using the FOIL Method.
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 and combine like terms.
Step 1.3.1
Simplify each term.
Step 1.3.1.1
Multiply by by adding the exponents.
Step 1.3.1.1.1
Move .
Step 1.3.1.1.2
Multiply by .
Step 1.3.1.2
Multiply by .
Step 1.3.1.3
Rewrite as .
Step 1.3.1.4
Multiply by .
Step 1.3.2
Subtract from .
Step 2
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 3
Step 3.1
Rewrite the equation as .
Step 3.2
Subtract from both sides of the equation.
Step 3.3
Subtract from .
Step 3.4
Factor by grouping.
Step 3.4.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Step 3.4.1.1
Factor out of .
Step 3.4.1.2
Rewrite as plus
Step 3.4.1.3
Apply the distributive property.
Step 3.4.2
Factor out the greatest common factor from each group.
Step 3.4.2.1
Group the first two terms and the last two terms.
Step 3.4.2.2
Factor out the greatest common factor (GCF) from each group.
Step 3.4.3
Factor the polynomial by factoring out the greatest common factor, .
Step 3.5
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.6
Set equal to and solve for .
Step 3.6.1
Set equal to .
Step 3.6.2
Solve for .
Step 3.6.2.1
Add to both sides of the equation.
Step 3.6.2.2
Divide each term in by and simplify.
Step 3.6.2.2.1
Divide each term in by .
Step 3.6.2.2.2
Simplify the left side.
Step 3.6.2.2.2.1
Cancel the common factor of .
Step 3.6.2.2.2.1.1
Cancel the common factor.
Step 3.6.2.2.2.1.2
Divide by .
Step 3.7
Set equal to and solve for .
Step 3.7.1
Set equal to .
Step 3.7.2
Subtract from both sides of the equation.
Step 3.8
The final solution is all the values that make true.
Step 4
Exclude the solutions that do not make true.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: