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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 the numerator by the reciprocal of the denominator.
Step 1.1.4
Apply the distributive property.
Step 1.1.5
Multiply by .
Step 1.1.6
Cancel the common factor of .
Step 1.1.6.1
Move the leading negative in into the numerator.
Step 1.1.6.2
Cancel the common factor.
Step 1.1.6.3
Rewrite the expression.
Step 1.1.7
Rewrite as .
Step 1.1.8
Rewrite in terms of sines and cosines.
Step 1.1.9
Rewrite in terms of sines and cosines.
Step 1.1.10
Multiply the numerator by the reciprocal of the denominator.
Step 1.1.11
Multiply by .
Step 2
Step 2.1
Simplify .
Step 2.1.1
Rewrite in terms of sines and cosines.
Step 2.1.2
Combine and .
Step 2.1.3
Move the negative in front of the fraction.
Step 3
Multiply both sides of the equation by .
Step 4
Apply the distributive property.
Step 5
Step 5.1
Cancel the common factor of .
Step 5.1.1
Cancel the common factor.
Step 5.1.2
Rewrite the expression.
Step 5.2
Rewrite using the commutative property of multiplication.
Step 5.3
Multiply .
Step 5.3.1
Combine and .
Step 5.3.2
Raise to the power of .
Step 5.3.3
Raise to the power of .
Step 5.3.4
Use the power rule to combine exponents.
Step 5.3.5
Add and .
Step 6
Step 6.1
Factor out of .
Step 6.2
Cancel the common factor.
Step 6.3
Rewrite the expression.
Step 7
Rewrite using the commutative property of multiplication.
Step 8
Step 8.1
Factor out of .
Step 8.2
Cancel the common factor.
Step 8.3
Rewrite the expression.
Step 9
Multiply by .
Step 10
Add to both sides of the equation.
Step 11
Step 11.1
Simplify each term.
Step 11.1.1
Factor out of .
Step 11.1.2
Separate fractions.
Step 11.1.3
Convert from to .
Step 11.1.4
Convert from to .
Step 11.1.5
Combine and .
Step 11.2
To write as a fraction with a common denominator, multiply by .
Step 11.3
Combine the numerators over the common denominator.
Step 11.4
Simplify the numerator.
Step 11.4.1
Apply the distributive property.
Step 11.4.2
Multiply by .
Step 11.4.3
Rewrite in terms of sines and cosines, then cancel the common factors.
Step 11.4.3.1
Reorder and .
Step 11.4.3.2
Add parentheses.
Step 11.4.3.3
Rewrite in terms of sines and cosines.
Step 11.4.3.4
Cancel the common factors.
Step 11.4.4
Multiply by .
Step 11.5
Add and .
Step 12
Divide each term in the equation by .
Step 13
Multiply the numerator by the reciprocal of the denominator.
Step 14
Step 14.1
Rewrite in terms of sines and cosines.
Step 14.2
Multiply .
Step 14.2.1
Combine and .
Step 14.2.2
Raise to the power of .
Step 14.2.3
Raise to the power of .
Step 14.2.4
Use the power rule to combine exponents.
Step 14.2.5
Add and .
Step 15
Rewrite in terms of sines and cosines.
Step 16
Step 16.1
Multiply by .
Step 16.2
Combine.
Step 17
Apply the distributive property.
Step 18
Step 18.1
Cancel the common factor of .
Step 18.1.1
Cancel the common factor.
Step 18.1.2
Rewrite the expression.
Step 18.2
Cancel the common factor of .
Step 18.2.1
Move the leading negative in into the numerator.
Step 18.2.2
Cancel the common factor.
Step 18.2.3
Rewrite the expression.
Step 19
Step 19.1
Rearrange terms.
Step 19.2
Rearrange terms.
Step 19.3
Raise to the power of .
Step 19.4
Raise to the power of .
Step 19.5
Use the power rule to combine exponents.
Step 19.6
Add and .
Step 19.7
Apply pythagorean identity.
Step 19.8
Move to the left of .
Step 19.9
Rewrite as .
Step 20
Step 20.1
Multiply by .
Step 20.2
Cancel the common factor of and .
Step 20.2.1
Factor out of .
Step 20.2.2
Rewrite as .
Step 20.2.3
Factor out of .
Step 20.2.4
Rewrite as .
Step 20.2.5
Cancel the common factor.
Step 20.2.6
Divide by .
Step 21
Convert from to .
Step 22
Convert from to .
Step 23
Separate fractions.
Step 24
Convert from to .
Step 25
Divide by .
Step 26
Multiply by .
Step 27
Add and .
Step 28
Since , the equation will always be true for any value of .
All real numbers
Step 29
The result can be shown in multiple forms.
All real numbers
Interval Notation: