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Trigonometry Examples
Step 1
Subtract from both sides of the equation.
Step 2
Step 2.1
Simplify each term.
Step 2.1.1
Simplify the numerator.
Step 2.1.1.1
Since both terms are perfect cubes, factor using the sum of cubes formula, where and .
Step 2.1.1.2
Simplify.
Step 2.1.1.2.1
Rearrange terms.
Step 2.1.1.2.2
Apply pythagorean identity.
Step 2.1.2
Rewrite in terms of sines and cosines.
Step 2.1.3
Rewrite in terms of sines and cosines.
Step 2.1.4
Multiply the numerator and denominator of the fraction by .
Step 2.1.4.1
Multiply by .
Step 2.1.4.2
Combine.
Step 2.1.5
Apply the distributive property.
Step 2.1.6
Simplify by cancelling.
Step 2.1.6.1
Cancel the common factor of .
Step 2.1.6.1.1
Cancel the common factor.
Step 2.1.6.1.2
Rewrite the expression.
Step 2.1.6.2
Cancel the common factor of .
Step 2.1.6.2.1
Cancel the common factor.
Step 2.1.6.2.2
Rewrite the expression.
Step 2.1.7
Rewrite using the commutative property of multiplication.
Step 2.1.8
Simplify the denominator.
Step 2.1.8.1
Move to the left of .
Step 2.1.8.2
Rewrite as .
Step 2.2
To write as a fraction with a common denominator, multiply by .
Step 2.3
To write as a fraction with a common denominator, multiply by .
Step 2.4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 2.4.1
Multiply by .
Step 2.4.2
Multiply by .
Step 2.4.3
Reorder the factors of .
Step 2.5
Combine the numerators over the common denominator.
Step 2.6
Simplify the numerator.
Step 2.6.1
Expand using the FOIL Method.
Step 2.6.1.1
Apply the distributive property.
Step 2.6.1.2
Apply the distributive property.
Step 2.6.1.3
Apply the distributive property.
Step 2.6.2
Simplify each term.
Step 2.6.2.1
Rewrite using the commutative property of multiplication.
Step 2.6.2.2
Multiply .
Step 2.6.2.2.1
Raise to the power of .
Step 2.6.2.2.2
Raise to the power of .
Step 2.6.2.2.3
Use the power rule to combine exponents.
Step 2.6.2.2.4
Add and .
Step 2.6.2.3
Multiply by .
Step 2.6.2.4
Rewrite using the commutative property of multiplication.
Step 2.6.2.5
Multiply .
Step 2.6.2.5.1
Raise to the power of .
Step 2.6.2.5.2
Raise to the power of .
Step 2.6.2.5.3
Use the power rule to combine exponents.
Step 2.6.2.5.4
Add and .
Step 2.6.2.6
Multiply by .
Step 2.6.3
Expand by multiplying each term in the first expression by each term in the second expression.
Step 2.6.4
Combine the opposite terms in .
Step 2.6.4.1
Reorder the factors in the terms and .
Step 2.6.4.2
Add and .
Step 2.6.4.3
Add and .
Step 2.6.5
Simplify each term.
Step 2.6.5.1
Multiply by by adding the exponents.
Step 2.6.5.1.1
Move .
Step 2.6.5.1.2
Multiply by .
Step 2.6.5.1.2.1
Raise to the power of .
Step 2.6.5.1.2.2
Use the power rule to combine exponents.
Step 2.6.5.1.3
Add and .
Step 2.6.5.2
Multiply .
Step 2.6.5.2.1
Multiply by .
Step 2.6.5.2.2
Multiply by .
Step 2.6.5.2.3
Raise to the power of .
Step 2.6.5.2.4
Raise to the power of .
Step 2.6.5.2.5
Use the power rule to combine exponents.
Step 2.6.5.2.6
Add and .
Step 2.6.5.3
Multiply .
Step 2.6.5.3.1
Raise to the power of .
Step 2.6.5.3.2
Raise to the power of .
Step 2.6.5.3.3
Use the power rule to combine exponents.
Step 2.6.5.3.4
Add and .
Step 2.6.5.4
Multiply .
Step 2.6.5.4.1
Raise to the power of .
Step 2.6.5.4.2
Raise to the power of .
Step 2.6.5.4.3
Use the power rule to combine exponents.
Step 2.6.5.4.4
Add and .
Step 2.6.5.5
Multiply by by adding the exponents.
Step 2.6.5.5.1
Move .
Step 2.6.5.5.2
Multiply by .
Step 2.6.5.5.2.1
Raise to the power of .
Step 2.6.5.5.2.2
Use the power rule to combine exponents.
Step 2.6.5.5.3
Add and .
Step 2.6.5.6
Multiply .
Step 2.6.5.6.1
Multiply by .
Step 2.6.5.6.2
Multiply by .
Step 2.6.5.7
Rewrite using the commutative property of multiplication.
Step 2.6.5.8
Multiply .
Step 2.6.5.8.1
Raise to the power of .
Step 2.6.5.8.2
Raise to the power of .
Step 2.6.5.8.3
Use the power rule to combine exponents.
Step 2.6.5.8.4
Add and .
Step 2.6.6
Combine the opposite terms in .
Step 2.6.6.1
Reorder the factors in the terms and .
Step 2.6.6.2
Subtract from .
Step 2.6.6.3
Add and .
Step 2.6.7
Apply the distributive property.
Step 2.6.8
Multiply by .
Step 2.6.9
Multiply .
Step 2.6.9.1
Multiply by .
Step 2.6.9.2
Multiply by .
Step 2.6.10
Expand using the FOIL Method.
Step 2.6.10.1
Apply the distributive property.
Step 2.6.10.2
Apply the distributive property.
Step 2.6.10.3
Apply the distributive property.
Step 2.6.11
Simplify each term.
Step 2.6.11.1
Multiply by .
Step 2.6.11.2
Multiply by .
Step 2.6.11.3
Multiply by .
Step 2.6.11.4
Rewrite using the commutative property of multiplication.
Step 2.6.11.5
Multiply by by adding the exponents.
Step 2.6.11.5.1
Move .
Step 2.6.11.5.2
Multiply by .
Step 2.6.11.5.2.1
Raise to the power of .
Step 2.6.11.5.2.2
Use the power rule to combine exponents.
Step 2.6.11.5.3
Add and .
Step 2.6.12
Subtract from .
Step 2.6.13
Add and .
Step 2.6.14
Rewrite in a factored form.
Step 2.6.14.1
Rearrange terms.
Step 2.6.14.2
Apply pythagorean identity.
Step 2.6.14.3
Add and .
Step 2.6.14.4
Add and .
Step 2.6.14.5
Rewrite in a factored form.
Step 2.6.14.5.1
Factor out of .
Step 2.6.14.5.1.1
Factor out of .
Step 2.6.14.5.1.2
Factor out of .
Step 2.6.14.5.1.3
Factor out of .
Step 2.6.14.5.1.4
Factor out of .
Step 2.6.14.5.1.5
Factor out of .
Step 2.6.14.5.2
Factor out of .
Step 2.6.14.5.3
Factor out of .
Step 2.6.14.5.4
Factor out of .
Step 2.6.14.5.5
Apply pythagorean identity.
Step 2.6.14.5.6
Multiply by .
Step 2.6.15
Add and .
Step 2.6.16
Combine exponents.
Step 2.6.16.1
Multiply by .
Step 2.6.16.2
Multiply by .
Step 2.7
Divide by .
Step 3
Since , the equation will always be true for any value of .
All real numbers
Step 4
The result can be shown in multiple forms.
All real numbers
Interval Notation: