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Trigonometry Examples
Step 1
Subtract from both sides of the equation.
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
Since contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .
Step 2.3
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
Step 2.4
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 2.5
Since has no factors besides and .
is a prime number
Step 2.6
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 2.7
The factor for is itself.
occurs time.
Step 2.8
The factors for are , which is multiplied by each other times.
occurs times.
Step 2.9
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 2.10
Multiply by .
Step 2.11
The LCM for is the numeric part multiplied by the variable part.
Step 3
Step 3.1
Multiply each term in by .
Step 3.2
Simplify the left side.
Step 3.2.1
Rewrite using the commutative property of multiplication.
Step 3.2.2
Combine and .
Step 3.2.3
Cancel the common factor of .
Step 3.2.3.1
Factor out of .
Step 3.2.3.2
Cancel the common factor.
Step 3.2.3.3
Rewrite the expression.
Step 3.3
Simplify the right side.
Step 3.3.1
Simplify each term.
Step 3.3.1.1
Rewrite using the commutative property of multiplication.
Step 3.3.1.2
Multiply .
Step 3.3.1.2.1
Combine and .
Step 3.3.1.2.2
Multiply by .
Step 3.3.1.3
Cancel the common factor of .
Step 3.3.1.3.1
Cancel the common factor.
Step 3.3.1.3.2
Rewrite the expression.
Step 3.3.1.4
Cancel the common factor of .
Step 3.3.1.4.1
Move the leading negative in into the numerator.
Step 3.3.1.4.2
Factor out of .
Step 3.3.1.4.3
Cancel the common factor.
Step 3.3.1.4.4
Rewrite the expression.
Step 4
Step 4.1
Add to both sides of the equation.
Step 4.2
Subtract from both sides of the equation.
Step 4.3
Factor the left side of the equation.
Step 4.3.1
Let . Substitute for all occurrences of .
Step 4.3.2
Factor using the AC method.
Step 4.3.2.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 4.3.2.2
Write the factored form using these integers.
Step 4.3.3
Replace all occurrences of with .
Step 4.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.5
Set equal to and solve for .
Step 4.5.1
Set equal to .
Step 4.5.2
Add to both sides of the equation.
Step 4.6
Set equal to and solve for .
Step 4.6.1
Set equal to .
Step 4.6.2
Subtract from both sides of the equation.
Step 4.7
The final solution is all the values that make true.