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Trigonometry Examples
Step 1
Step 1.1
Multiply the numerator by the reciprocal of the denominator.
Step 1.2
Multiply by .
Step 1.3
Move to the left of .
Step 1.4
Multiply by .
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
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 2.3
Since has no factors besides and .
is a prime 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
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 2.6
The factor for is itself.
occurs time.
Step 2.7
The factor for is itself.
occurs time.
Step 2.8
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Step 2.9
The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.
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
Cancel the common factor of .
Step 3.2.2.1
Cancel the common factor.
Step 3.2.2.2
Rewrite the expression.
Step 3.2.3
Cancel the common factor of .
Step 3.2.3.1
Cancel the common factor.
Step 3.2.3.2
Rewrite the expression.
Step 3.2.4
Apply the distributive property.
Step 3.2.5
Multiply by by adding the exponents.
Step 3.2.5.1
Move .
Step 3.2.5.2
Multiply by .
Step 3.2.6
Multiply by .
Step 3.3
Simplify the right side.
Step 3.3.1
Simplify terms.
Step 3.3.1.1
Rewrite using the commutative property of multiplication.
Step 3.3.1.2
Combine and .
Step 3.3.1.3
Cancel the common factor of .
Step 3.3.1.3.1
Factor out of .
Step 3.3.1.3.2
Cancel the common factor.
Step 3.3.1.3.3
Rewrite the expression.
Step 3.3.1.4
Apply the distributive property.
Step 3.3.1.5
Multiply.
Step 3.3.1.5.1
Multiply by .
Step 3.3.1.5.2
Multiply by .
Step 3.3.2
Expand using the FOIL Method.
Step 3.3.2.1
Apply the distributive property.
Step 3.3.2.2
Apply the distributive property.
Step 3.3.2.3
Apply the distributive property.
Step 3.3.3
Simplify and combine like terms.
Step 3.3.3.1
Simplify each term.
Step 3.3.3.1.1
Multiply by by adding the exponents.
Step 3.3.3.1.1.1
Move .
Step 3.3.3.1.1.2
Multiply by .
Step 3.3.3.1.2
Multiply by .
Step 3.3.3.1.3
Multiply by .
Step 3.3.3.2
Subtract from .
Step 4
Step 4.1
Move all terms containing to the left side of the equation.
Step 4.1.1
Subtract from both sides of the equation.
Step 4.1.2
Add to both sides of the equation.
Step 4.1.3
Subtract from .
Step 4.1.4
Add and .
Step 4.2
Subtract from both sides of the equation.
Step 4.3
Use the quadratic formula to find the solutions.
Step 4.4
Substitute the values , , and into the quadratic formula and solve for .
Step 4.5
Simplify.
Step 4.5.1
Simplify the numerator.
Step 4.5.1.1
Raise to the power of .
Step 4.5.1.2
Multiply .
Step 4.5.1.2.1
Multiply by .
Step 4.5.1.2.2
Multiply by .
Step 4.5.1.3
Subtract from .
Step 4.5.2
Multiply by .
Step 4.5.3
Simplify .
Step 4.6
The final answer is the combination of both solutions.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: