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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 1.1.3
Multiply by the reciprocal of the fraction to divide by .
Step 1.1.4
Write as a fraction with denominator .
Step 1.1.5
Simplify.
Step 1.1.5.1
Divide by .
Step 1.1.5.2
Combine and .
Step 1.1.6
Simplify the numerator.
Step 1.1.6.1
Raise to the power of .
Step 1.1.6.2
Raise to the power of .
Step 1.1.6.3
Use the power rule to combine exponents.
Step 1.1.6.4
Add and .
Step 2
Step 2.1
Simplify .
Step 2.1.1
Rewrite in terms of sines and cosines.
Step 2.1.2
Multiply the numerator by the reciprocal of the denominator.
Step 2.1.3
Apply the distributive property.
Step 2.1.4
Multiply by .
Step 2.1.5
Multiply .
Step 2.1.5.1
Combine and .
Step 2.1.5.2
Raise to the power of .
Step 2.1.5.3
Raise to the power of .
Step 2.1.5.4
Use the power rule to combine exponents.
Step 2.1.5.5
Add and .
Step 3
Multiply both sides of the equation by .
Step 4
Apply the distributive property.
Step 5
Step 5.1
Cancel the common factor.
Step 5.2
Rewrite the expression.
Step 6
Rewrite using the commutative property of multiplication.
Step 7
Step 7.1
Factor out of .
Step 7.2
Cancel the common factor.
Step 7.3
Rewrite the expression.
Step 8
Apply the distributive property.
Step 9
Step 9.1
Cancel the common factor.
Step 9.2
Rewrite the expression.
Step 10
Rewrite using the commutative property of multiplication.
Step 11
Step 11.1
Factor out of .
Step 11.2
Cancel the common factor.
Step 11.3
Rewrite the expression.
Step 12
Step 12.1
Subtract from both sides of the equation.
Step 12.2
Add to both sides of the equation.
Step 12.3
Combine the opposite terms in .
Step 12.3.1
Subtract from .
Step 12.3.2
Add and .
Step 12.3.3
Add and .
Step 13
Since , the equation will always be true for any value of .
All real numbers
Step 14
The result can be shown in multiple forms.
All real numbers
Interval Notation: