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Trigonometry Examples
Step 1
Step 1.1
Simplify each term.
Step 1.1.1
Rewrite in terms of sines and cosines.
Step 1.1.2
Rewrite in terms of sines and cosines.
Step 2
Multiply both sides of the equation by .
Step 3
Apply the distributive property.
Step 4
Step 4.1
Cancel the common factor.
Step 4.2
Rewrite the expression.
Step 5
Step 5.1
Cancel the common factor.
Step 5.2
Rewrite the expression.
Step 6
Step 6.1
Combine and .
Step 6.2
Raise to the power of .
Step 6.3
Raise to the power of .
Step 6.4
Use the power rule to combine exponents.
Step 6.5
Add and .
Step 7
Subtract from both sides of the equation.
Step 8
Step 8.1
To write as a fraction with a common denominator, multiply by .
Step 8.2
Combine the numerators over the common denominator.
Step 8.3
Simplify each term.
Step 8.3.1
Simplify the numerator.
Step 8.3.1.1
Apply the distributive property.
Step 8.3.1.2
Multiply by .
Step 8.3.1.3
Rewrite using the commutative property of multiplication.
Step 8.3.1.4
Multiply .
Step 8.3.1.4.1
Raise to the power of .
Step 8.3.1.4.2
Raise to the power of .
Step 8.3.1.4.3
Use the power rule to combine exponents.
Step 8.3.1.4.4
Add and .
Step 8.3.1.5
Factor out of .
Step 8.3.1.6
Factor out of .
Step 8.3.1.7
Factor out of .
Step 8.3.1.8
Apply pythagorean identity.
Step 8.3.1.9
Multiply by .
Step 8.3.2
Cancel the common factor of and .
Step 8.3.2.1
Factor out of .
Step 8.3.2.2
Rewrite as .
Step 8.3.2.3
Factor out of .
Step 8.3.2.4
Reorder terms.
Step 8.3.2.5
Cancel the common factor.
Step 8.3.2.6
Divide by .
Step 8.4
Subtract from .
Step 9
Since , the equation will always be true for any value of .
All real numbers
Step 10
The result can be shown in multiple forms.
All real numbers
Interval Notation: