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Trigonometry Examples
Step 1
Step 1.1
Simplify .
Step 1.1.1
To write as a fraction with a common denominator, multiply by .
Step 1.1.2
To write as a fraction with a common denominator, multiply by .
Step 1.1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 1.1.3.1
Multiply by .
Step 1.1.3.2
Multiply by .
Step 1.1.3.3
Reorder the factors of .
Step 1.1.4
Combine the numerators over the common denominator.
Step 1.1.5
Simplify the numerator.
Step 1.1.5.1
Add and .
Step 1.1.5.2
Subtract from .
Step 1.1.5.3
Add and .
Step 2
Multiply both sides by .
Step 3
Step 3.1
Simplify the left side.
Step 3.1.1
Cancel the common factor of .
Step 3.1.1.1
Cancel the common factor.
Step 3.1.1.2
Rewrite the expression.
Step 3.2
Simplify the right side.
Step 3.2.1
Simplify .
Step 3.2.1.1
Rewrite in terms of sines and cosines.
Step 3.2.1.2
Combine fractions.
Step 3.2.1.2.1
Apply the product rule to .
Step 3.2.1.2.2
One to any power is one.
Step 3.2.1.2.3
Combine and .
Step 3.2.1.3
Expand using the FOIL Method.
Step 3.2.1.3.1
Apply the distributive property.
Step 3.2.1.3.2
Apply the distributive property.
Step 3.2.1.3.3
Apply the distributive property.
Step 3.2.1.4
Simplify and combine like terms.
Step 3.2.1.4.1
Simplify each term.
Step 3.2.1.4.1.1
Multiply by .
Step 3.2.1.4.1.2
Multiply by .
Step 3.2.1.4.1.3
Multiply by .
Step 3.2.1.4.1.4
Rewrite using the commutative property of multiplication.
Step 3.2.1.4.1.5
Multiply .
Step 3.2.1.4.1.5.1
Raise to the power of .
Step 3.2.1.4.1.5.2
Raise to the power of .
Step 3.2.1.4.1.5.3
Use the power rule to combine exponents.
Step 3.2.1.4.1.5.4
Add and .
Step 3.2.1.4.2
Add and .
Step 3.2.1.4.3
Add and .
Step 3.2.1.5
Apply pythagorean identity.
Step 3.2.1.6
Cancel the common factor of .
Step 3.2.1.6.1
Cancel the common factor.
Step 3.2.1.6.2
Rewrite the expression.
Step 4
Since , the equation will always be true for any value of .
All real numbers
Step 5
The result can be shown in multiple forms.
All real numbers
Interval Notation: