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Trigonometry Examples
Step 1
Step 1.1
Divide each term in by .
Step 1.2
Simplify the left side.
Step 1.2.1
Cancel the common factor of .
Step 1.2.1.1
Cancel the common factor.
Step 1.2.1.2
Divide by .
Step 2
Interchange the variables.
Step 3
Step 3.1
Rewrite the equation as .
Step 3.2
Multiply both sides of the equation by .
Step 3.3
Simplify both sides of the equation.
Step 3.3.1
Simplify the left side.
Step 3.3.1.1
Simplify .
Step 3.3.1.1.1
Cancel the common factor of .
Step 3.3.1.1.1.1
Cancel the common factor.
Step 3.3.1.1.1.2
Rewrite the expression.
Step 3.3.1.1.2
Cancel the common factor of .
Step 3.3.1.1.2.1
Factor out of .
Step 3.3.1.1.2.2
Cancel the common factor.
Step 3.3.1.1.2.3
Rewrite the expression.
Step 3.3.2
Simplify the right side.
Step 3.3.2.1
Combine and .
Step 4
Replace with to show the final answer.
Step 5
Step 5.1
To verify the inverse, check if and .
Step 5.2
Evaluate .
Step 5.2.1
Set up the composite result function.
Step 5.2.2
Evaluate by substituting in the value of into .
Step 5.2.3
Combine and .
Step 5.2.4
Multiply by .
Step 5.2.5
Reduce the expression by cancelling the common factors.
Step 5.2.5.1
Reduce the expression by cancelling the common factors.
Step 5.2.5.1.1
Factor out of .
Step 5.2.5.1.2
Factor out of .
Step 5.2.5.1.3
Cancel the common factor.
Step 5.2.5.1.4
Rewrite the expression.
Step 5.2.5.2
Divide by .
Step 5.2.6
Cancel the common factor of .
Step 5.2.6.1
Cancel the common factor.
Step 5.2.6.2
Divide by .
Step 5.3
Evaluate .
Step 5.3.1
Set up the composite result function.
Step 5.3.2
Evaluate by substituting in the value of into .
Step 5.3.3
Combine and .
Step 5.3.4
Multiply by .
Step 5.3.5
Reduce the expression by cancelling the common factors.
Step 5.3.5.1
Reduce the expression by cancelling the common factors.
Step 5.3.5.1.1
Factor out of .
Step 5.3.5.1.2
Factor out of .
Step 5.3.5.1.3
Cancel the common factor.
Step 5.3.5.1.4
Rewrite the expression.
Step 5.3.5.2
Divide by .
Step 5.3.6
Cancel the common factor of .
Step 5.3.6.1
Cancel the common factor.
Step 5.3.6.2
Divide by .
Step 5.4
Since and , then is the inverse of .