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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
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 prime factors the greatest number of times they occur in either term.
Step 2.9
Multiply by .
Step 3
Step 3.1
Multiply each term in by .
Step 3.2
Simplify the left side.
Step 3.2.1
Cancel the common factor of .
Step 3.2.1.1
Factor out of .
Step 3.2.1.2
Cancel the common factor.
Step 3.2.1.3
Rewrite the expression.
Step 3.3
Simplify the right side.
Step 3.3.1
Simplify each term.
Step 3.3.1.1
Multiply by .
Step 3.3.1.2
Cancel the common factor of .
Step 3.3.1.2.1
Move the leading negative in into the numerator.
Step 3.3.1.2.2
Factor out of .
Step 3.3.1.2.3
Cancel the common factor.
Step 3.3.1.2.4
Rewrite the expression.
Step 4
Step 4.1
Rewrite the equation as .
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 4.3
Divide each term in by and simplify.
Step 4.3.1
Divide each term in by .
Step 4.3.2
Simplify the left side.
Step 4.3.2.1
Cancel the common factor of .
Step 4.3.2.1.1
Cancel the common factor.
Step 4.3.2.1.2
Divide by .
Step 5
Interchange the variables.
Step 6
Step 6.1
Multiply the equation by .
Step 6.2
Simplify the left side.
Step 6.2.1
Simplify .
Step 6.2.1.1
Apply the distributive property.
Step 6.2.1.2
Rewrite as .
Step 6.3
Simplify the right side.
Step 6.3.1
Cancel the common factor of .
Step 6.3.1.1
Cancel the common factor.
Step 6.3.1.2
Rewrite the expression.
Step 6.4
Solve for .
Step 6.4.1
Subtract from both sides of the equation.
Step 6.4.2
Add to both sides of the equation.
Step 6.4.3
Factor out of .
Step 6.4.3.1
Factor out of .
Step 6.4.3.2
Factor out of .
Step 6.4.3.3
Factor out of .
Step 6.4.4
Divide each term in by and simplify.
Step 6.4.4.1
Divide each term in by .
Step 6.4.4.2
Simplify the left side.
Step 6.4.4.2.1
Cancel the common factor of .
Step 6.4.4.2.1.1
Cancel the common factor.
Step 6.4.4.2.1.2
Divide by .
Step 7
Replace with to show the final answer.
Step 8
Step 8.1
To verify the inverse, check if and .
Step 8.2
Evaluate .
Step 8.2.1
Set up the composite result function.
Step 8.2.2
Evaluate by substituting in the value of into .
Step 8.2.3
Multiply the numerator by the reciprocal of the denominator.
Step 8.2.4
Simplify the denominator.
Step 8.2.4.1
To write as a fraction with a common denominator, multiply by .
Step 8.2.4.2
Combine and .
Step 8.2.4.3
Combine the numerators over the common denominator.
Step 8.2.4.4
Rewrite in a factored form.
Step 8.2.4.4.1
Apply the distributive property.
Step 8.2.4.4.2
Multiply by .
Step 8.2.4.4.3
Subtract from .
Step 8.2.4.4.4
Add and .
Step 8.2.5
Multiply the numerator by the reciprocal of the denominator.
Step 8.2.6
Cancel the common factor of .
Step 8.2.6.1
Factor out of .
Step 8.2.6.2
Cancel the common factor.
Step 8.2.6.3
Rewrite the expression.
Step 8.3
Evaluate .
Step 8.3.1
Set up the composite result function.
Step 8.3.2
Evaluate by substituting in the value of into .
Step 8.3.3
Multiply the numerator by the reciprocal of the denominator.
Step 8.3.4
Simplify the denominator.
Step 8.3.4.1
To write as a fraction with a common denominator, multiply by .
Step 8.3.4.2
Combine and .
Step 8.3.4.3
Combine the numerators over the common denominator.
Step 8.3.4.4
Rewrite in a factored form.
Step 8.3.4.4.1
Apply the distributive property.
Step 8.3.4.4.2
Multiply by .
Step 8.3.4.4.3
Subtract from .
Step 8.3.4.4.4
Add and .
Step 8.3.5
Multiply the numerator by the reciprocal of the denominator.
Step 8.3.6
Cancel the common factor of .
Step 8.3.6.1
Factor out of .
Step 8.3.6.2
Cancel the common factor.
Step 8.3.6.3
Rewrite the expression.
Step 8.4
Since and , then is the inverse of .