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Trigonometry Examples
Step 1
Interchange the variables.
Step 2
Step 2.1
Rewrite the equation as .
Step 2.2
Add to both sides of the equation.
Step 2.3
Find the LCD of the terms in the equation.
Step 2.3.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.3.2
The LCM of one and any expression is the expression.
Step 2.4
Multiply each term in by to eliminate the fractions.
Step 2.4.1
Multiply each term in by .
Step 2.4.2
Simplify the left side.
Step 2.4.2.1
Cancel the common factor of .
Step 2.4.2.1.1
Cancel the common factor.
Step 2.4.2.1.2
Rewrite the expression.
Step 2.5
Solve the equation.
Step 2.5.1
Rewrite the equation as .
Step 2.5.2
Factor out of .
Step 2.5.2.1
Factor out of .
Step 2.5.2.2
Factor out of .
Step 2.5.2.3
Factor out of .
Step 2.5.3
Divide each term in by and simplify.
Step 2.5.3.1
Divide each term in by .
Step 2.5.3.2
Simplify the left side.
Step 2.5.3.2.1
Cancel the common factor of .
Step 2.5.3.2.1.1
Cancel the common factor.
Step 2.5.3.2.1.2
Divide by .
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 the denominator.
Step 4.2.3.1
Add and .
Step 4.2.3.2
Add and .
Step 4.2.4
Multiply the numerator by the reciprocal of the denominator.
Step 4.2.5
Cancel the common factor of .
Step 4.2.5.1
Cancel the common factor.
Step 4.2.5.2
Rewrite the expression.
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 each term.
Step 4.3.3.1
Multiply the numerator by the reciprocal of the denominator.
Step 4.3.3.2
Cancel the common factor of .
Step 4.3.3.2.1
Cancel the common factor.
Step 4.3.3.2.2
Rewrite the expression.
Step 4.3.4
Combine the opposite terms in .
Step 4.3.4.1
Subtract from .
Step 4.3.4.2
Add and .
Step 4.4
Since and , then is the inverse of .