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Trigonometry Examples
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
Step 4.1
The exact value of is .
Step 4.2
The exact value of is .
Step 4.3
Multiply by .
Step 5
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
Step 7.1
Multiply by .
Step 7.2
Expand the denominator using the FOIL method.
Step 7.3
Simplify.
Step 8
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
Step 10.1
Apply the distributive property.
Step 10.2
Apply the distributive property.
Step 10.3
Apply the distributive property.
Step 11
Step 11.1
Simplify each term.
Step 11.1.1
Multiply by .
Step 11.1.2
Multiply by .
Step 11.1.3
Multiply by .
Step 11.1.4
Multiply .
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 .
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 .
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
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
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: