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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
Combine and .
Step 5.2
Raise to the power of .
Step 5.3
Raise to the power of .
Step 5.4
Use the power rule to combine exponents.
Step 5.5
Add and .
Step 6
Combine and .
Step 7
Apply the sine double-angle identity.
Step 8
Step 8.1
Cancel the common factor.
Step 8.2
Rewrite the expression.
Step 9
Step 9.1
Cancel the common factor.
Step 9.2
Rewrite the expression.
Step 10
Subtract from both sides of the equation.
Step 11
Step 11.1
Combine the numerators over the common denominator.
Step 11.2
Reorder and .
Step 11.3
Rewrite as .
Step 11.4
Factor out of .
Step 11.5
Factor out of .
Step 11.6
Rewrite as .
Step 11.7
Apply pythagorean identity.
Step 11.8
Cancel the common factor of and .
Step 11.8.1
Factor out of .
Step 11.8.2
Cancel the common factors.
Step 11.8.2.1
Multiply by .
Step 11.8.2.2
Cancel the common factor.
Step 11.8.2.3
Rewrite the expression.
Step 11.8.2.4
Divide by .
Step 11.9
Subtract from .
Step 12
Since , the equation will always be true for any value of .
All real numbers
Step 13
The result can be shown in multiple forms.
All real numbers
Interval Notation: