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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
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
Move the leading negative in into the numerator.
Step 2.3.2.1.2
Factor out of .
Step 2.3.2.1.3
Cancel the common factor.
Step 2.3.2.1.4
Rewrite the expression.
Step 2.3.2.2
Cancel the common factor of .
Step 2.3.2.2.1
Cancel the common factor.
Step 2.3.2.2.2
Rewrite the expression.
Step 2.4
Solve the equation.
Step 2.4.1
Rewrite the equation as .
Step 2.4.2
Divide each term in by and simplify.
Step 2.4.2.1
Divide each term in by .
Step 2.4.2.2
Simplify the left side.
Step 2.4.2.2.1
Cancel the common factor of .
Step 2.4.2.2.1.1
Cancel the common factor.
Step 2.4.2.2.1.2
Divide by .
Step 2.4.2.3
Simplify the right side.
Step 2.4.2.3.1
Multiply the numerator by the reciprocal of the denominator.
Step 2.4.2.3.2
Multiply by .
Step 2.4.2.3.3
Move to the left of .
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
Cancel the common factor of and .
Step 4.2.3.1
Rewrite as .
Step 4.2.3.2
Move the negative in front of the fraction.
Step 4.2.4
Combine and .
Step 4.2.5
Multiply.
Step 4.2.5.1
Multiply by .
Step 4.2.5.2
Simplify.
Step 4.2.5.2.1
Multiply the numerator by the reciprocal of the denominator.
Step 4.2.5.2.2
Multiply 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
Multiply the numerator by the reciprocal of the denominator.
Step 4.3.4
Multiply by .
Step 4.3.5
Multiply by .
Step 4.4
Since and , then is the inverse of .