Trigonometry Examples

Expand Using Sum/Difference Formulas tan(pi/12)
Step 1
First, split the angle into two angles where the values of the six trigonometric functions are known. In this case, can be split into .
Step 2
Use the difference formula for tangent to simplify the expression. The formula states that .
Step 3
Remove parentheses.
Step 4
Simplify the numerator.
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Step 4.1
The exact value of is .
Step 4.2
The exact value of is .
Step 4.3
Multiply by .
Step 5
Simplify the denominator.
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Step 5.1
The exact value of is .
Step 5.2
The exact value of is .
Step 5.3
Multiply by .
Step 6
Multiply by .
Step 7
Combine fractions.
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Step 7.1
Multiply by .
Step 7.2
Expand the denominator using the FOIL method.
Step 7.3
Simplify.
Step 8
Simplify the numerator.
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Step 8.1
Factor out of .
Step 8.2
Rewrite as .
Step 8.3
Factor out of .
Step 8.4
Reorder terms.
Step 8.5
Raise to the power of .
Step 8.6
Raise to the power of .
Step 8.7
Use the power rule to combine exponents.
Step 8.8
Add and .
Step 9
Rewrite as .
Step 10
Expand using the FOIL Method.
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Step 10.1
Apply the distributive property.
Step 10.2
Apply the distributive property.
Step 10.3
Apply the distributive property.
Step 11
Simplify and combine like terms.
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Step 11.1
Simplify each term.
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Step 11.1.1
Multiply by .
Step 11.1.2
Multiply by .
Step 11.1.3
Multiply by .
Step 11.1.4
Multiply .
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Step 11.1.4.1
Multiply by .
Step 11.1.4.2
Multiply by .
Step 11.1.4.3
Raise to the power of .
Step 11.1.4.4
Raise to the power of .
Step 11.1.4.5
Use the power rule to combine exponents.
Step 11.1.4.6
Add and .
Step 11.1.5
Rewrite as .
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Step 11.1.5.1
Use to rewrite as .
Step 11.1.5.2
Apply the power rule and multiply exponents, .
Step 11.1.5.3
Combine and .
Step 11.1.5.4
Cancel the common factor of .
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Step 11.1.5.4.1
Cancel the common factor.
Step 11.1.5.4.2
Rewrite the expression.
Step 11.1.5.5
Evaluate the exponent.
Step 11.2
Add and .
Step 11.3
Subtract from .
Step 12
Cancel the common factor of and .
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Step 12.1
Factor out of .
Step 12.2
Move the negative one from the denominator of .
Step 13
Rewrite as .
Step 14
Apply the distributive property.
Step 15
Multiply by .
Step 16
Multiply .
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Step 16.1
Multiply by .
Step 16.2
Multiply by .
Step 17
Apply the distributive property.
Step 18
Multiply by .
Step 19
The result can be shown in multiple forms.
Exact Form:
Decimal Form: