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Trigonometry Examples
Step 1
Multiply both sides by .
Step 2
Step 2.1
Simplify the left side.
Step 2.1.1
Simplify .
Step 2.1.1.1
Rewrite in terms of sines and cosines.
Step 2.1.1.2
Simplify terms.
Step 2.1.1.2.1
Apply the distributive property.
Step 2.1.1.2.2
Simplify the expression.
Step 2.1.1.2.2.1
Multiply by .
Step 2.1.1.2.2.2
Rewrite using the commutative property of multiplication.
Step 2.1.1.2.3
Combine and .
Step 2.1.1.3
Simplify each term.
Step 2.1.1.3.1
Convert from to .
Step 2.1.1.3.2
Separate fractions.
Step 2.1.1.3.3
Rewrite as a product.
Step 2.1.1.3.4
Write as a fraction with denominator .
Step 2.1.1.3.5
Simplify.
Step 2.1.1.3.5.1
Divide by .
Step 2.1.1.3.5.2
Convert from to .
Step 2.1.1.3.6
Divide by .
Step 2.2
Simplify the right side.
Step 2.2.1
Cancel the common factor of .
Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Rewrite the expression.
Step 3
Step 3.1
Simplify the left side.
Step 3.1.1
Simplify each term.
Step 3.1.1.1
Rewrite in terms of sines and cosines.
Step 3.1.1.2
Rewrite in terms of sines and cosines.
Step 3.1.1.3
Multiply .
Step 3.1.1.3.1
Combine and .
Step 3.1.1.3.2
Combine and .
Step 3.2
Multiply both sides of the equation by .
Step 3.3
Apply the distributive property.
Step 3.4
Cancel the common factor of .
Step 3.4.1
Cancel the common factor.
Step 3.4.2
Rewrite the expression.
Step 3.5
Rewrite using the commutative property of multiplication.
Step 3.6
Cancel the common factor of .
Step 3.6.1
Factor out of .
Step 3.6.2
Cancel the common factor.
Step 3.6.3
Rewrite the expression.
Step 3.7
Use the double-angle identity to transform to .
Step 3.8
Subtract from both sides of the equation.
Step 3.9
Simplify the left side.
Step 3.9.1
Simplify .
Step 3.9.1.1
Simplify each term.
Step 3.9.1.1.1
Apply the distributive property.
Step 3.9.1.1.2
Multiply by .
Step 3.9.1.1.3
Multiply by .
Step 3.9.1.1.4
Apply the distributive property.
Step 3.9.1.1.5
Rewrite as .
Step 3.9.1.1.6
Apply the sine double-angle identity.
Step 3.9.1.1.7
Multiply .
Step 3.9.1.1.7.1
Multiply by .
Step 3.9.1.1.7.2
Raise to the power of .
Step 3.9.1.1.7.3
Raise to the power of .
Step 3.9.1.1.7.4
Use the power rule to combine exponents.
Step 3.9.1.1.7.5
Add and .
Step 3.9.1.2
Combine the opposite terms in .
Step 3.9.1.2.1
Subtract from .
Step 3.9.1.2.2
Subtract from .
Step 3.9.1.2.3
Add and .
Step 3.10
Since , the equation will always be true for any value of .
All real numbers
All real numbers
Step 4
The result can be shown in multiple forms.
All real numbers
Interval Notation: