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# Trigonometry Examples

Interchange the variables.

Rewrite the equation as .

Subtract from both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.

Take the root of both sides of the to eliminate the exponent on the left side.

The complete solution is the result of both the positive and negative portions of the solution.

Simplify the right side of the equation.

Combine the numerators over the common denominator.

Rewrite as .

Multiply by .

Combine and simplify the denominator.

Multiply and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Evaluate the exponent.

Combine using the product rule for radicals.

Reorder factors in .

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the to find the first solution.

Next, use the negative value of the to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

Replace the with to show the final answer.

Set up the composite result function.

Evaluate by substituting in the value of into .

Simplify the numerator.

Subtract from .

Add and .

Multiply by .

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Since , is the inverse of .