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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
Rewrite as .
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
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
Step 9.1
Subtract from both sides of the equation.
Step 9.2
Add to both sides of the equation.
Step 10
Step 10.1
Simplify each term.
Step 10.1.1
Factor out of .
Step 10.1.2
Separate fractions.
Step 10.1.3
Convert from to .
Step 10.1.4
Convert from to .
Step 10.1.5
Combine and .
Step 10.2
To write as a fraction with a common denominator, multiply by .
Step 10.3
Combine the numerators over the common denominator.
Step 10.4
Simplify the numerator.
Step 10.4.1
Apply the distributive property.
Step 10.4.2
Multiply by .
Step 10.4.3
Rewrite in terms of sines and cosines, then cancel the common factors.
Step 10.4.3.1
Reorder and .
Step 10.4.3.2
Rewrite in terms of sines and cosines.
Step 10.4.3.3
Cancel the common factors.
Step 11
Divide each term in the equation by .
Step 12
Multiply the numerator by the reciprocal of the denominator.
Step 13
Step 13.1
Rewrite in terms of sines and cosines.
Step 13.2
Multiply .
Step 13.2.1
Combine and .
Step 13.2.2
Raise to the power of .
Step 13.2.3
Raise to the power of .
Step 13.2.4
Use the power rule to combine exponents.
Step 13.2.5
Add and .
Step 14
Rewrite in terms of sines and cosines.
Step 15
Step 15.1
Multiply by .
Step 15.2
Combine.
Step 16
Apply the distributive property.
Step 17
Step 17.1
Cancel the common factor of .
Step 17.1.1
Cancel the common factor.
Step 17.1.2
Rewrite the expression.
Step 17.2
Cancel the common factor of .
Step 17.2.1
Cancel the common factor.
Step 17.2.2
Rewrite the expression.
Step 18
Step 18.1
Rearrange terms.
Step 18.2
Raise to the power of .
Step 18.3
Raise to the power of .
Step 18.4
Use the power rule to combine exponents.
Step 18.5
Add and .
Step 18.6
Apply pythagorean identity.
Step 18.7
Multiply by .
Step 19
Step 19.1
Multiply by .
Step 19.2
Cancel the common factor of and .
Step 19.2.1
Reorder terms.
Step 19.2.2
Cancel the common factor.
Step 19.2.3
Rewrite the expression.
Step 19.3
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: