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Trigonometry Examples
Step 1
Rewrite using the commutative property of multiplication.
Step 2
Step 2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.2
Remove parentheses.
Step 2.3
The LCM of one and any expression is the expression.
Step 3
Step 3.1
Multiply each term in by .
Step 3.2
Simplify the left side.
Step 3.2.1
Apply the distributive property.
Step 3.2.2
Multiply by by adding the exponents.
Step 3.2.2.1
Move .
Step 3.2.2.2
Multiply by .
Step 3.2.2.2.1
Raise to the power of .
Step 3.2.2.2.2
Use the power rule to combine exponents.
Step 3.2.2.3
Add and .
Step 3.2.3
Multiply by .
Step 3.2.4
Multiply by .
Step 3.3
Simplify the right side.
Step 3.3.1
Cancel the common factor of .
Step 3.3.1.1
Cancel the common factor.
Step 3.3.1.2
Rewrite the expression.
Step 4
Step 4.1
Subtract from both sides of the equation.
Step 4.2
Factor out of .
Step 4.2.1
Factor out of .
Step 4.2.2
Factor out of .
Step 4.2.3
Factor out of .
Step 4.2.4
Factor out of .
Step 4.2.5
Factor out of .
Step 4.3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.4
Set equal to .
Step 4.5
Set equal to and solve for .
Step 4.5.1
Set equal to .
Step 4.5.2
Solve for .
Step 4.5.2.1
Move all terms not containing to the right side of the equation.
Step 4.5.2.1.1
Subtract from both sides of the equation.
Step 4.5.2.1.2
Add to both sides of the equation.
Step 4.5.2.2
Divide each term in by and simplify.
Step 4.5.2.2.1
Divide each term in by .
Step 4.5.2.2.2
Simplify the left side.
Step 4.5.2.2.2.1
Cancel the common factor of .
Step 4.5.2.2.2.1.1
Cancel the common factor.
Step 4.5.2.2.2.1.2
Rewrite the expression.
Step 4.5.2.2.2.2
Cancel the common factor of .
Step 4.5.2.2.2.2.1
Cancel the common factor.
Step 4.5.2.2.2.2.2
Divide by .
Step 4.5.2.2.3
Simplify the right side.
Step 4.5.2.2.3.1
Simplify each term.
Step 4.5.2.2.3.1.1
Cancel the common factor of .
Step 4.5.2.2.3.1.1.1
Cancel the common factor.
Step 4.5.2.2.3.1.1.2
Rewrite the expression.
Step 4.5.2.2.3.1.2
Move the negative in front of the fraction.
Step 4.5.2.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 4.5.2.4
Simplify .
Step 4.5.2.4.1
To write as a fraction with a common denominator, multiply by .
Step 4.5.2.4.2
Multiply by .
Step 4.5.2.4.3
Combine the numerators over the common denominator.
Step 4.5.2.4.4
Rewrite as .
Step 4.5.2.4.5
Multiply by .
Step 4.5.2.4.6
Combine and simplify the denominator.
Step 4.5.2.4.6.1
Multiply by .
Step 4.5.2.4.6.2
Raise to the power of .
Step 4.5.2.4.6.3
Raise to the power of .
Step 4.5.2.4.6.4
Use the power rule to combine exponents.
Step 4.5.2.4.6.5
Add and .
Step 4.5.2.4.6.6
Rewrite as .
Step 4.5.2.4.6.6.1
Use to rewrite as .
Step 4.5.2.4.6.6.2
Apply the power rule and multiply exponents, .
Step 4.5.2.4.6.6.3
Combine and .
Step 4.5.2.4.6.6.4
Cancel the common factor of .
Step 4.5.2.4.6.6.4.1
Cancel the common factor.
Step 4.5.2.4.6.6.4.2
Rewrite the expression.
Step 4.5.2.4.6.6.5
Simplify.
Step 4.5.2.4.7
Combine using the product rule for radicals.
Step 4.5.2.4.8
Reorder factors in .
Step 4.5.2.5
The complete solution is the result of both the positive and negative portions of the solution.
Step 4.5.2.5.1
First, use the positive value of the to find the first solution.
Step 4.5.2.5.2
Next, use the negative value of the to find the second solution.
Step 4.5.2.5.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 4.6
The final solution is all the values that make true.