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Trigonometry Examples
Step 1
Step 1.1
Simplify .
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
Multiply by .
Step 2
Step 2.1
Simplify .
Step 2.1.1
Rewrite in terms of sines and cosines.
Step 2.1.2
Rewrite in terms of sines and cosines.
Step 2.1.3
Multiply the numerator by the reciprocal of the denominator.
Step 2.1.4
Apply the distributive property.
Step 2.1.5
Cancel the common factor of .
Step 2.1.5.1
Cancel the common factor.
Step 2.1.5.2
Rewrite the expression.
Step 2.1.6
Multiply by .
Step 3
Multiply both sides of the equation by .
Step 4
Step 4.1
Combine and .
Step 4.2
Raise to the power of .
Step 4.3
Raise to the power of .
Step 4.4
Use the power rule to combine exponents.
Step 4.5
Add and .
Step 5
Apply the distributive property.
Step 6
Step 6.1
Cancel the common factor.
Step 6.2
Rewrite the expression.
Step 7
Step 7.1
Cancel the common factor.
Step 7.2
Rewrite the expression.
Step 8
Step 8.1
Subtract from both sides of the equation.
Step 8.2
Subtract from both sides of the equation.
Step 9
Step 9.1
Simplify each term.
Step 9.1.1
Factor out of .
Step 9.1.2
Separate fractions.
Step 9.1.3
Convert from to .
Step 9.1.4
Convert from to .
Step 9.1.5
Combine and .
Step 9.2
To write as a fraction with a common denominator, multiply by .
Step 9.3
Combine and .
Step 9.4
Combine the numerators over the common denominator.
Step 9.5
Simplify the numerator.
Step 9.5.1
Apply the distributive property.
Step 9.5.2
Rewrite in terms of sines and cosines, then cancel the common factors.
Step 9.5.2.1
Add parentheses.
Step 9.5.2.2
Reorder and .
Step 9.5.2.3
Rewrite in terms of sines and cosines.
Step 9.5.2.4
Cancel the common factors.
Step 9.5.3
Multiply .
Step 9.5.3.1
Multiply by .
Step 9.5.3.2
Multiply by .
Step 9.5.4
Multiply by .
Step 10
Divide each term in the equation by .
Step 11
Multiply the numerator by the reciprocal of the denominator.
Step 12
Step 12.1
Rewrite in terms of sines and cosines.
Step 12.2
Multiply .
Step 12.2.1
Combine and .
Step 12.2.2
Raise to the power of .
Step 12.2.3
Raise to the power of .
Step 12.2.4
Use the power rule to combine exponents.
Step 12.2.5
Add and .
Step 13
Rewrite in terms of sines and cosines.
Step 14
Step 14.1
Multiply by .
Step 14.2
Combine.
Step 15
Apply the distributive property.
Step 16
Step 16.1
Cancel the common factor of .
Step 16.1.1
Cancel the common factor.
Step 16.1.2
Rewrite the expression.
Step 16.2
Cancel the common factor of .
Step 16.2.1
Cancel the common factor.
Step 16.2.2
Rewrite the expression.
Step 17
Step 17.1
Rearrange terms.
Step 17.2
Rearrange terms.
Step 17.3
Raise to the power of .
Step 17.4
Raise to the power of .
Step 17.5
Use the power rule to combine exponents.
Step 17.6
Add and .
Step 17.7
Apply pythagorean identity.
Step 17.8
Move to the left of .
Step 17.9
Rewrite as .
Step 18
Step 18.1
Move to the left of .
Step 18.2
Rewrite as .
Step 19
Step 19.1
Cancel the common factor of and .
Step 19.1.1
Reorder terms.
Step 19.1.2
Cancel the common factor.
Step 19.1.3
Rewrite the expression.
Step 19.2
Multiply by .
Step 20
Convert from to .
Step 21
Separate fractions.
Step 22
Convert from to .
Step 23
Divide by .
Step 24
Separate fractions.
Step 25
Convert from to .
Step 26
Divide by .
Step 27
Multiply by .
Step 28
Subtract from .
Step 29
Since , the equation will always be true for any value of .
All real numbers
Step 30
The result can be shown in multiple forms.
All real numbers
Interval Notation: