Expand Using Sum/Difference Formulas tan(-195)

Math
First, split the angle into two angles where the values of the six trigonometric functions are known. In this case, can be split into .
Use the difference formula for tangent to simplify the expression. The formula states that .
Simplify the numerator.
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The exact value of is .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
Simplify the denominator.
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The exact value of is .
Multiply by .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
Multiply by .
Combine fractions.
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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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Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
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 .
Move the negative one from the denominator of .
Rewrite as .
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:
Expand Using Sum/Difference Formulas tan(-195)


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