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Trigonometry Examples
Step 1
Interchange the variables.
Step 2
Step 2.1
Multiply the equation by .
Step 2.2
Simplify the left side.
Step 2.2.1
Apply the distributive property.
Step 2.3
Simplify the right side.
Step 2.3.1
Simplify .
Step 2.3.1.1
Cancel the common factor of .
Step 2.3.1.1.1
Move the leading negative in into the numerator.
Step 2.3.1.1.2
Cancel the common factor.
Step 2.3.1.1.3
Rewrite the expression.
Step 2.3.1.2
Apply the distributive property.
Step 2.3.1.3
Multiply by .
Step 2.4
Solve for .
Step 2.4.1
Add to both sides of the equation.
Step 2.4.2
Add to both sides of the equation.
Step 2.4.3
Factor out of .
Step 2.4.3.1
Factor out of .
Step 2.4.3.2
Raise to the power of .
Step 2.4.3.3
Factor out of .
Step 2.4.3.4
Factor out of .
Step 2.4.4
Divide each term in by and simplify.
Step 2.4.4.1
Divide each term in by .
Step 2.4.4.2
Simplify the left side.
Step 2.4.4.2.1
Cancel the common factor of .
Step 2.4.4.2.1.1
Cancel the common factor.
Step 2.4.4.2.1.2
Divide by .
Step 2.4.4.3
Simplify the right side.
Step 2.4.4.3.1
Combine the numerators over the common denominator.
Step 2.4.4.3.2
Rewrite as .
Step 2.4.4.3.3
Factor out of .
Step 2.4.4.3.4
Factor out of .
Step 2.4.4.3.5
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 the numerator.
Step 4.2.3.1
Multiply .
Step 4.2.3.1.1
Multiply by .
Step 4.2.3.1.2
Combine and .
Step 4.2.3.2
To write as a fraction with a common denominator, multiply by .
Step 4.2.3.3
Combine the numerators over the common denominator.
Step 4.2.3.4
Reorder terms.
Step 4.2.3.5
Rewrite in a factored form.
Step 4.2.3.5.1
Apply the distributive property.
Step 4.2.3.5.2
Multiply by .
Step 4.2.3.5.3
Apply the distributive property.
Step 4.2.3.5.4
Multiply by .
Step 4.2.3.5.5
Multiply by .
Step 4.2.3.5.6
Add and .
Step 4.2.3.5.7
Subtract from .
Step 4.2.3.5.8
Add and .
Step 4.2.4
Simplify the denominator.
Step 4.2.4.1
Multiply .
Step 4.2.4.1.1
Multiply by .
Step 4.2.4.1.2
Combine and .
Step 4.2.4.2
Move the negative in front of the fraction.
Step 4.2.4.3
Write as a fraction with a common denominator.
Step 4.2.4.4
Combine the numerators over the common denominator.
Step 4.2.4.5
Reorder terms.
Step 4.2.4.6
Rewrite in a factored form.
Step 4.2.4.6.1
Apply the distributive property.
Step 4.2.4.6.2
Multiply by .
Step 4.2.4.6.3
Subtract from .
Step 4.2.4.6.4
Subtract from .
Step 4.2.4.6.5
Subtract from .
Step 4.2.4.7
Move the negative in front of the fraction.
Step 4.2.5
Multiply the numerator by the reciprocal of the denominator.
Step 4.2.6
Rewrite using the commutative property of multiplication.
Step 4.2.7
Cancel the common factor of .
Step 4.2.7.1
Move the leading negative in into the numerator.
Step 4.2.7.2
Factor out of .
Step 4.2.7.3
Cancel the common factor.
Step 4.2.7.4
Rewrite the expression.
Step 4.2.8
Cancel the common factor of .
Step 4.2.8.1
Cancel the common factor.
Step 4.2.8.2
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
Multiply the numerator and denominator of the fraction by .
Step 4.3.3.1
Multiply by .
Step 4.3.3.2
Combine.
Step 4.3.4
Apply the distributive property.
Step 4.3.5
Cancel the common factor of .
Step 4.3.5.1
Move the leading negative in into the numerator.
Step 4.3.5.2
Cancel the common factor.
Step 4.3.5.3
Rewrite the expression.
Step 4.3.6
Simplify the numerator.
Step 4.3.6.1
Apply the distributive property.
Step 4.3.6.2
Multiply by .
Step 4.3.6.3
Multiply by .
Step 4.3.6.4
Apply the distributive property.
Step 4.3.6.5
Multiply by .
Step 4.3.6.6
Multiply by .
Step 4.3.6.7
Add and .
Step 4.3.6.8
Add and .
Step 4.3.6.9
Add and .
Step 4.3.7
Simplify the denominator.
Step 4.3.7.1
Factor out of .
Step 4.3.7.1.1
Factor out of .
Step 4.3.7.1.2
Factor out of .
Step 4.3.7.2
Multiply .
Step 4.3.7.2.1
Multiply by .
Step 4.3.7.2.2
Combine and .
Step 4.3.7.3
Move the negative in front of the fraction.
Step 4.3.7.4
To write as a fraction with a common denominator, multiply by .
Step 4.3.7.5
Combine and .
Step 4.3.7.6
Combine the numerators over the common denominator.
Step 4.3.7.7
Rewrite in a factored form.
Step 4.3.7.7.1
Factor out of .
Step 4.3.7.7.1.1
Reorder and .
Step 4.3.7.7.1.2
Factor out of .
Step 4.3.7.7.1.3
Factor out of .
Step 4.3.7.7.1.4
Factor out of .
Step 4.3.7.7.2
Apply the distributive property.
Step 4.3.7.7.3
Multiply by .
Step 4.3.7.7.4
Multiply by .
Step 4.3.7.7.5
Apply the distributive property.
Step 4.3.7.7.6
Multiply by .
Step 4.3.7.7.7
Multiply by .
Step 4.3.7.7.8
Add and .
Step 4.3.7.7.9
Add and .
Step 4.3.7.7.10
Add and .
Step 4.3.7.8
Multiply by .
Step 4.3.7.9
Move the negative in front of the fraction.
Step 4.3.7.10
Factor out negative.
Step 4.3.8
Factor out of .
Step 4.3.9
Cancel the common factor of .
Step 4.3.9.1
Factor out of .
Step 4.3.9.2
Cancel the common factor.
Step 4.3.9.3
Rewrite the expression.
Step 4.3.10
Cancel the common factor of .
Step 4.3.10.1
Factor out of .
Step 4.3.10.2
Cancel the common factor.
Step 4.3.10.3
Rewrite the expression.
Step 4.3.11
Simplify the expression.
Step 4.3.11.1
Move the negative one from the denominator of .
Step 4.3.11.2
Rewrite as .
Step 4.4
Since and , then is the inverse of .