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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 2.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.4
Simplify .
Step 2.4.1
Rewrite as .
Step 2.4.1.1
Factor the perfect power out of .
Step 2.4.1.2
Factor the perfect power out of .
Step 2.4.1.3
Rearrange the fraction .
Step 2.4.2
Pull terms out from under the radical.
Step 2.4.3
Combine and .
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
Rewrite as .
Step 4.2.3.2
Pull terms out from under the radical, assuming real numbers.
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
Apply the product rule to .
Step 4.3.4
Rewrite as .
Step 4.3.4.1
Use to rewrite as .
Step 4.3.4.2
Apply the power rule and multiply exponents, .
Step 4.3.4.3
Combine and .
Step 4.3.4.4
Cancel the common factor of .
Step 4.3.4.4.1
Cancel the common factor.
Step 4.3.4.4.2
Rewrite the expression.
Step 4.3.4.5
Simplify.
Step 4.3.5
Raise to the power of .
Step 4.3.6
Cancel the common factor of .
Step 4.3.6.1
Cancel the common factor.
Step 4.3.6.2
Rewrite the expression.
Step 4.4
Since and , then is the inverse of .