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Trigonometry Examples
Step 1
Subtract from both sides of the equation.
Step 2
Step 2.1
Apply the cosine double-angle identity.
Step 2.2
Simplify each term.
Step 2.2.1
Rearrange terms.
Step 2.2.2
Apply pythagorean identity.
Step 2.2.3
Simplify the numerator.
Step 2.2.3.1
Rewrite as .
Step 2.2.3.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2.2.3.3
Simplify.
Step 2.2.3.3.1
Rewrite in terms of sines and cosines.
Step 2.2.3.3.2
Rewrite in terms of sines and cosines.
Step 2.2.4
Simplify the denominator.
Step 2.2.4.1
Rewrite in terms of sines and cosines.
Step 2.2.4.2
Apply the product rule to .
Step 2.2.4.3
One to any power is one.
Step 2.2.5
Multiply the numerator by the reciprocal of the denominator.
Step 2.2.6
Expand using the FOIL Method.
Step 2.2.6.1
Apply the distributive property.
Step 2.2.6.2
Apply the distributive property.
Step 2.2.6.3
Apply the distributive property.
Step 2.2.7
Simplify and combine like terms.
Step 2.2.7.1
Simplify each term.
Step 2.2.7.1.1
Multiply by .
Step 2.2.7.1.2
Multiply by .
Step 2.2.7.1.3
Multiply by .
Step 2.2.7.1.4
Rewrite using the commutative property of multiplication.
Step 2.2.7.1.5
Multiply .
Step 2.2.7.1.5.1
Multiply by .
Step 2.2.7.1.5.2
Raise to the power of .
Step 2.2.7.1.5.3
Raise to the power of .
Step 2.2.7.1.5.4
Use the power rule to combine exponents.
Step 2.2.7.1.5.5
Add and .
Step 2.2.7.1.5.6
Raise to the power of .
Step 2.2.7.1.5.7
Raise to the power of .
Step 2.2.7.1.5.8
Use the power rule to combine exponents.
Step 2.2.7.1.5.9
Add and .
Step 2.2.7.2
Add and .
Step 2.2.7.3
Add and .
Step 2.2.8
Apply the distributive property.
Step 2.2.9
Multiply by .
Step 2.2.10
Cancel the common factor of .
Step 2.2.10.1
Move the leading negative in into the numerator.
Step 2.2.10.2
Cancel the common factor.
Step 2.2.10.3
Rewrite the expression.
Step 2.2.11
Apply the cosine double-angle identity.
Step 2.3
Subtract from .
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: