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Trigonometry Examples
Step 1
Interchange the variables.
Step 2
Step 2.1
Rewrite the equation as .
Step 2.2
Divide each term in by and simplify.
Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
Step 2.2.2.1
Cancel the common factor of .
Step 2.2.2.1.1
Cancel the common factor.
Step 2.2.2.1.2
Divide by .
Step 2.2.3
Simplify the right side.
Step 2.2.3.1
Move the negative in front of the fraction.
Step 2.3
To remove the radical on the left side of the equation, square both sides of the equation.
Step 2.4
Simplify each side of the equation.
Step 2.4.1
Use to rewrite as .
Step 2.4.2
Simplify the left side.
Step 2.4.2.1
Simplify .
Step 2.4.2.1.1
Multiply the exponents in .
Step 2.4.2.1.1.1
Apply the power rule and multiply exponents, .
Step 2.4.2.1.1.2
Cancel the common factor of .
Step 2.4.2.1.1.2.1
Cancel the common factor.
Step 2.4.2.1.1.2.2
Rewrite the expression.
Step 2.4.2.1.2
Simplify.
Step 2.4.3
Simplify the right side.
Step 2.4.3.1
Simplify .
Step 2.4.3.1.1
Use the power rule to distribute the exponent.
Step 2.4.3.1.1.1
Apply the product rule to .
Step 2.4.3.1.1.2
Apply the product rule to .
Step 2.4.3.1.2
Raise to the power of .
Step 2.4.3.1.3
Multiply by .
Step 2.4.3.1.4
Raise to the power 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
Simplify the numerator.
Step 4.2.3.1
Apply the product rule to .
Step 4.2.3.2
Raise to the power of .
Step 4.2.3.3
Rewrite as .
Step 4.2.3.3.1
Use to rewrite as .
Step 4.2.3.3.2
Apply the power rule and multiply exponents, .
Step 4.2.3.3.3
Combine and .
Step 4.2.3.3.4
Cancel the common factor of .
Step 4.2.3.3.4.1
Cancel the common factor.
Step 4.2.3.3.4.2
Rewrite the expression.
Step 4.2.3.3.5
Simplify.
Step 4.2.4
Cancel the common factor of .
Step 4.2.4.1
Cancel the common factor.
Step 4.2.4.2
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
Remove parentheses.
Step 4.3.4
Rewrite as .
Step 4.3.5
Rewrite as .
Step 4.3.6
Pull terms out from under the radical, assuming positive real numbers.
Step 4.3.7
Cancel the common factor of .
Step 4.3.7.1
Factor out of .
Step 4.3.7.2
Cancel the common factor.
Step 4.3.7.3
Rewrite the expression.
Step 4.3.8
Rewrite as .
Step 4.4
Since and , then is the inverse of .