Trigonometry Examples

Simplify Using Half-Angle Formula tan(165 degrees )
Step 1
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 second quadrant.
Step 2
Split into two angles where the values of the six trigonometric functions are known.
Step 3
Separate negation.
Step 4
Apply the difference of angles identity.
Step 5
The exact value of is .
Step 6
The exact value of is .
Step 7
The exact value of is .
Step 8
The exact value of is .
Step 9
Simplify .
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Step 9.1
Multiply the numerator and denominator of the fraction by .
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Step 9.1.1
Multiply by .
Step 9.1.2
Combine.
Step 9.2
Apply the distributive property.
Step 9.3
Cancel the common factor of .
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Step 9.3.1
Move the leading negative in into the numerator.
Step 9.3.2
Cancel the common factor.
Step 9.3.3
Rewrite the expression.
Step 9.4
Multiply by .
Step 9.5
Simplify the denominator.
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Step 9.5.1
Multiply by .
Step 9.5.2
Cancel the common factor of .
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Step 9.5.2.1
Factor out of .
Step 9.5.2.2
Cancel the common factor.
Step 9.5.2.3
Rewrite the expression.
Step 9.6
Multiply by .
Step 9.7
Multiply by .
Step 9.8
Expand the denominator using the FOIL method.
Step 9.9
Simplify.
Step 9.10
Simplify the numerator.
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Step 9.10.1
Raise to the power of .
Step 9.10.2
Raise to the power of .
Step 9.10.3
Use the power rule to combine exponents.
Step 9.10.4
Add and .
Step 9.11
Rewrite as .
Step 9.12
Expand using the FOIL Method.
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Step 9.12.1
Apply the distributive property.
Step 9.12.2
Apply the distributive property.
Step 9.12.3
Apply the distributive property.
Step 9.13
Simplify and combine like terms.
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Step 9.13.1
Simplify each term.
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Step 9.13.1.1
Multiply by .
Step 9.13.1.2
Multiply by .
Step 9.13.1.3
Multiply by .
Step 9.13.1.4
Multiply .
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Step 9.13.1.4.1
Multiply by .
Step 9.13.1.4.2
Multiply by .
Step 9.13.1.4.3
Raise to the power of .
Step 9.13.1.4.4
Raise to the power of .
Step 9.13.1.4.5
Use the power rule to combine exponents.
Step 9.13.1.4.6
Add and .
Step 9.13.1.5
Rewrite as .
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Step 9.13.1.5.1
Use to rewrite as .
Step 9.13.1.5.2
Apply the power rule and multiply exponents, .
Step 9.13.1.5.3
Combine and .
Step 9.13.1.5.4
Cancel the common factor of .
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Step 9.13.1.5.4.1
Cancel the common factor.
Step 9.13.1.5.4.2
Rewrite the expression.
Step 9.13.1.5.5
Evaluate the exponent.
Step 9.13.2
Add and .
Step 9.13.3
Subtract from .
Step 9.14
Cancel the common factor of and .
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Step 9.14.1
Factor out of .
Step 9.14.2
Factor out of .
Step 9.14.3
Factor out of .
Step 9.14.4
Cancel the common factors.
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Step 9.14.4.1
Factor out of .
Step 9.14.4.2
Cancel the common factor.
Step 9.14.4.3
Rewrite the expression.
Step 9.14.4.4
Divide by .
Step 9.15
Apply the distributive property.
Step 9.16
Multiply by .
Step 9.17
Multiply .
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Step 9.17.1
Multiply by .
Step 9.17.2
Multiply by .
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form: