# Find the Exact Value tan(-15 degrees )

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the fourth quadrant.

Split into two angles where the values of the six trigonometric functions are known.

Separate negation.

Apply the difference of angles identity.

The exact value of is .

The exact value of is .

The exact value of is .

The exact value of is .

Simplify .

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Multiply the numerator and denominator of the complex fraction by .

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Multiply by .

Combine.

Apply the distributive property.

Cancel the common factor of .

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Move the leading negative in into the numerator.

Cancel the common factor.

Rewrite the expression.

Multiply by .

Simplify the denominator.

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Multiply by .

Cancel the common factor of .

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Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Multiply and .

Expand the denominator using the FOIL method.

Simplify.

Simplify the numerator.

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Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Expand using the FOIL Method.

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Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

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Simplify each term.

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Multiply by .

Multiply by .

Multiply by .

Multiply .

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Multiply by .

Multiply by .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

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Use to rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

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Cancel the common factor.

Rewrite the expression.

Evaluate the exponent.

Add and .

Subtract from .

Cancel the common factor of and .

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Factor out of .

Factor out of .

Factor out of .

Cancel the common factors.

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Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Apply the distributive property.

Multiply by .

Multiply .

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Multiply by .

Multiply by .

The result can be shown in multiple forms.

Exact Form:

Decimal Form: