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Trigonometry Examples
Step 1
Interchange the variables.
Step 2
Step 2.1
Rewrite the equation as .
Step 2.2
Multiply by by adding the exponents.
Step 2.2.1
Move .
Step 2.2.2
Multiply by .
Step 2.2.2.1
Raise to the power of .
Step 2.2.2.2
Use the power rule to combine exponents.
Step 2.2.3
Add and .
Step 2.3
Move all terms not containing to the right side of the equation.
Step 2.3.1
Subtract from both sides of the equation.
Step 2.3.2
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
Simplify each term.
Step 2.4.3.1.1
Cancel the common factor of and .
Step 2.4.3.1.1.1
Factor out of .
Step 2.4.3.1.1.2
Cancel the common factors.
Step 2.4.3.1.1.2.1
Factor out of .
Step 2.4.3.1.1.2.2
Cancel the common factor.
Step 2.4.3.1.1.2.3
Rewrite the expression.
Step 2.4.3.1.2
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 terms.
Step 4.2.3.1
Combine the numerators over the common denominator.
Step 4.2.3.2
Combine the opposite terms in .
Step 4.2.3.2.1
Add and .
Step 4.2.3.2.2
Add and .
Step 4.2.3.3
Reorder factors in .
Step 4.2.4
Simplify each term.
Step 4.2.4.1
Factor out of .
Step 4.2.4.1.1
Factor out of .
Step 4.2.4.1.2
Factor out of .
Step 4.2.4.1.3
Factor out of .
Step 4.2.4.2
Cancel the common factors.
Step 4.2.4.2.1
Factor out of .
Step 4.2.4.2.2
Cancel the common factor.
Step 4.2.4.2.3
Rewrite the expression.
Step 4.2.4.3
Move the negative in front of the fraction.
Step 4.2.5
Simplify terms.
Step 4.2.5.1
Combine the numerators over the common denominator.
Step 4.2.5.2
Combine the opposite terms in .
Step 4.2.5.2.1
Subtract from .
Step 4.2.5.2.2
Add and .
Step 4.2.5.3
Cancel the common factor of and .
Step 4.2.5.3.1
Factor out of .
Step 4.2.5.3.2
Cancel the common factors.
Step 4.2.5.3.2.1
Factor out of .
Step 4.2.5.3.2.2
Cancel the common factor.
Step 4.2.5.3.2.3
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 by by adding the exponents.
Step 4.3.3.1.1
Move .
Step 4.3.3.1.2
Multiply by .
Step 4.3.3.1.2.1
Raise to the power of .
Step 4.3.3.1.2.2
Use the power rule to combine exponents.
Step 4.3.3.1.3
Add and .
Step 4.3.3.2
Apply the distributive property.
Step 4.3.3.3
Simplify.
Step 4.3.3.3.1
Cancel the common factor of .
Step 4.3.3.3.1.1
Cancel the common factor.
Step 4.3.3.3.1.2
Rewrite the expression.
Step 4.3.3.3.2
Cancel the common factor of .
Step 4.3.3.3.2.1
Move the leading negative in into the numerator.
Step 4.3.3.3.2.2
Factor out of .
Step 4.3.3.3.2.3
Cancel the common factor.
Step 4.3.3.3.2.4
Rewrite the expression.
Step 4.3.3.3.3
Cancel the common factor of .
Step 4.3.3.3.3.1
Cancel the common factor.
Step 4.3.3.3.3.2
Rewrite the expression.
Step 4.3.4
Combine the opposite terms in .
Step 4.3.4.1
Add and .
Step 4.3.4.2
Add and .
Step 4.3.4.3
Subtract from .
Step 4.3.4.4
Add and .
Step 4.4
Since and , then is the inverse of .