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Trigonometry Examples
Step 1
Interchange the variables.
Step 2
Step 2.1
Rewrite the equation as .
Step 2.2
Find the LCD of the terms in the equation.
Step 2.2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.2.2
Remove parentheses.
Step 2.2.3
The LCM of one and any expression is the expression.
Step 2.3
Multiply each term in by to eliminate the fractions.
Step 2.3.1
Multiply each term in by .
Step 2.3.2
Simplify the left side.
Step 2.3.2.1
Cancel the common factor of .
Step 2.3.2.1.1
Cancel the common factor.
Step 2.3.2.1.2
Rewrite the expression.
Step 2.3.3
Simplify the right side.
Step 2.3.3.1
Apply the distributive property.
Step 2.3.3.2
Simplify the expression.
Step 2.3.3.2.1
Rewrite using the commutative property of multiplication.
Step 2.3.3.2.2
Multiply by .
Step 2.4
Solve the equation.
Step 2.4.1
Rewrite the equation as .
Step 2.4.2
Subtract from both sides of the equation.
Step 2.4.3
Divide each term in by and simplify.
Step 2.4.3.1
Divide each term in by .
Step 2.4.3.2
Simplify the left side.
Step 2.4.3.2.1
Cancel the common factor of .
Step 2.4.3.2.1.1
Cancel the common factor.
Step 2.4.3.2.1.2
Rewrite the expression.
Step 2.4.3.2.2
Cancel the common factor of .
Step 2.4.3.2.2.1
Cancel the common factor.
Step 2.4.3.2.2.2
Divide by .
Step 2.4.3.3
Simplify the right side.
Step 2.4.3.3.1
Simplify each term.
Step 2.4.3.3.1.1
Cancel the common factor of .
Step 2.4.3.3.1.1.1
Cancel the common factor.
Step 2.4.3.3.1.1.2
Rewrite the expression.
Step 2.4.3.3.1.2
Move the negative in front of the fraction.
Step 3
Replace with to show the final answer.
Step 4
Step 4.1
To verify the inverse, check if and .
Step 4.2
Evaluate .
Step 4.2.1
Set up the composite result function.
Step 4.2.2
Evaluate by substituting in the value of into .
Step 4.2.3
Simplify each term.
Step 4.2.3.1
Combine and .
Step 4.2.3.2
Multiply the numerator by the reciprocal of the denominator.
Step 4.2.3.3
Multiply by .
Step 4.2.4
Simplify terms.
Step 4.2.4.1
Combine the numerators over the common denominator.
Step 4.2.4.2
Combine the opposite terms in .
Step 4.2.4.2.1
Subtract from .
Step 4.2.4.2.2
Add and .
Step 4.2.4.3
Cancel the common factor of .
Step 4.2.4.3.1
Cancel the common factor.
Step 4.2.4.3.2
Divide by .
Step 4.3
Evaluate .
Step 4.3.1
Set up the composite result function.
Step 4.3.2
Evaluate by substituting in the value of into .
Step 4.3.3
Simplify the denominator.
Step 4.3.3.1
Apply the distributive property.
Step 4.3.3.2
Cancel the common factor of .
Step 4.3.3.2.1
Factor out of .
Step 4.3.3.2.2
Cancel the common factor.
Step 4.3.3.2.3
Rewrite the expression.
Step 4.3.3.3
Cancel the common factor of .
Step 4.3.3.3.1
Move the leading negative in into the numerator.
Step 4.3.3.3.2
Cancel the common factor.
Step 4.3.3.3.3
Rewrite the expression.
Step 4.3.3.4
Add and .
Step 4.3.3.5
Add and .
Step 4.3.4
Multiply the numerator by the reciprocal of the denominator.
Step 4.3.5
Multiply by .
Step 4.4
Since and , then is the inverse of .