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# Trigonometry Examples

Interchange the variables.

Rewrite the equation as .

Subtract from both sides of the equation.

To remove the radical on the left side of the equation, square both sides of the equation.

Simplify each side of the equation.

Simplify the left side of the equation.

Simplify the right side of the equation.

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Move to the left of .

Rewrite as .

Rewrite as .

Multiply by .

Subtract from .

Solve for .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from .

Multiply each term in by

Multiply each term in by .

Multiply .

Multiply by .

Multiply by .

Simplify each term.

Move to the left of .

Rewrite as .

Multiply by .

Multiply by .

Replace the with to show the final answer.

Set up the composite result function.

Evaluate by substituting in the value of into .

Simplify each term.

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply .

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 .

Simplify.

Multiply by .

Multiply by .

Multiply by .

Add and .

Add and .

Apply the distributive property.

Simplify.

Multiply by .

Multiply .

Multiply by .

Multiply by .

Multiply by .

Apply the distributive property.

Multiply by .

Simplify by adding terms.

Combine the opposite terms in .

Add and .

Add and .

Add and .

Combine the opposite terms in .

Add and .

Add and .

Since , is the inverse of .