Enter a problem...
Trigonometry Examples
Step 1
Interchange the variables.
Step 2
Step 2.1
Rewrite the equation as .
Step 2.2
Simplify .
Step 2.2.1
Simplify each term.
Step 2.2.1.1
Apply the distributive property.
Step 2.2.1.2
Multiply by .
Step 2.2.1.3
Multiply by .
Step 2.2.2
Simplify by adding terms.
Step 2.2.2.1
Subtract from .
Step 2.2.2.2
Add and .
Step 2.3
Add to both sides of the equation.
Step 2.4
Divide each term in by and simplify.
Step 2.4.1
Divide 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
Divide by .
Step 2.4.3
Simplify the right side.
Step 2.4.3.1
Cancel the common factor of and .
Step 2.4.3.1.1
Factor out of .
Step 2.4.3.1.2
Cancel the common factors.
Step 2.4.3.1.2.1
Factor out of .
Step 2.4.3.1.2.2
Cancel the common factor.
Step 2.4.3.1.2.3
Rewrite the expression.
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
Cancel the common factor of and .
Step 4.2.3.1.1
Factor out of .
Step 4.2.3.1.2
Factor out of .
Step 4.2.3.1.3
Factor out of .
Step 4.2.3.1.4
Factor out of .
Step 4.2.3.1.5
Cancel the common factors.
Step 4.2.3.1.5.1
Factor out of .
Step 4.2.3.1.5.2
Cancel the common factor.
Step 4.2.3.1.5.3
Rewrite the expression.
Step 4.2.3.2
Simplify the numerator.
Step 4.2.3.2.1
Subtract from .
Step 4.2.3.2.2
Add and .
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
Add and .
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 each term.
Step 4.3.3.1
Simplify each term.
Step 4.3.3.1.1
Apply the distributive property.
Step 4.3.3.1.2
Cancel the common factor of .
Step 4.3.3.1.2.1
Factor out of .
Step 4.3.3.1.2.2
Factor out of .
Step 4.3.3.1.2.3
Cancel the common factor.
Step 4.3.3.1.2.4
Rewrite the expression.
Step 4.3.3.1.3
Combine and .
Step 4.3.3.1.4
Combine and .
Step 4.3.3.2
To write as a fraction with a common denominator, multiply by .
Step 4.3.3.3
Combine and .
Step 4.3.3.4
Combine the numerators over the common denominator.
Step 4.3.3.5
Simplify the numerator.
Step 4.3.3.5.1
Multiply by .
Step 4.3.3.5.2
Add and .
Step 4.3.3.6
Apply the distributive property.
Step 4.3.3.7
Multiply .
Step 4.3.3.7.1
Combine and .
Step 4.3.3.7.2
Multiply by .
Step 4.3.3.8
Multiply .
Step 4.3.3.8.1
Combine and .
Step 4.3.3.8.2
Multiply by .
Step 4.3.3.9
Apply the distributive property.
Step 4.3.3.10
Cancel the common factor of .
Step 4.3.3.10.1
Factor out of .
Step 4.3.3.10.2
Factor out of .
Step 4.3.3.10.3
Cancel the common factor.
Step 4.3.3.10.4
Rewrite the expression.
Step 4.3.3.11
Combine and .
Step 4.3.3.12
Combine and .
Step 4.3.4
Simplify terms.
Step 4.3.4.1
Combine the numerators over the common denominator.
Step 4.3.4.2
Add and .
Step 4.3.4.3
Add and .
Step 4.3.4.4
Cancel the common factor of and .
Step 4.3.4.4.1
Factor out of .
Step 4.3.4.4.2
Factor out of .
Step 4.3.4.4.3
Factor out of .
Step 4.3.4.4.4
Cancel the common factors.
Step 4.3.4.4.4.1
Factor out of .
Step 4.3.4.4.4.2
Cancel the common factor.
Step 4.3.4.4.4.3
Rewrite the expression.
Step 4.3.4.4.4.4
Divide by .
Step 4.3.4.5
Combine the opposite terms in .
Step 4.3.4.5.1
Add and .
Step 4.3.4.5.2
Add and .
Step 4.4
Since and , then is the inverse of .