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Trigonometry Examples
Step 1
Step 1.1
Simplify each term.
Step 1.1.1
The exact value of is .
Step 1.1.1.1
Split into two angles where the values of the six trigonometric functions are known.
Step 1.1.1.2
Separate negation.
Step 1.1.1.3
Apply the difference of angles identity.
Step 1.1.1.4
The exact value of is .
Step 1.1.1.5
The exact value of is .
Step 1.1.1.6
The exact value of is .
Step 1.1.1.7
The exact value of is .
Step 1.1.1.8
Simplify .
Step 1.1.1.8.1
Simplify each term.
Step 1.1.1.8.1.1
Multiply .
Step 1.1.1.8.1.1.1
Multiply by .
Step 1.1.1.8.1.1.2
Combine using the product rule for radicals.
Step 1.1.1.8.1.1.3
Multiply by .
Step 1.1.1.8.1.1.4
Multiply by .
Step 1.1.1.8.1.2
Multiply .
Step 1.1.1.8.1.2.1
Multiply by .
Step 1.1.1.8.1.2.2
Multiply by .
Step 1.1.1.8.2
Combine the numerators over the common denominator.
Step 1.1.2
The exact value of is .
Step 1.1.3
The exact value of is .
Step 1.1.3.1
Split into two angles where the values of the six trigonometric functions are known.
Step 1.1.3.2
Separate negation.
Step 1.1.3.3
Apply the difference of angles identity .
Step 1.1.3.4
The exact value of is .
Step 1.1.3.5
The exact value of is .
Step 1.1.3.6
The exact value of is .
Step 1.1.3.7
The exact value of is .
Step 1.1.3.8
Simplify .
Step 1.1.3.8.1
Simplify each term.
Step 1.1.3.8.1.1
Multiply .
Step 1.1.3.8.1.1.1
Multiply by .
Step 1.1.3.8.1.1.2
Combine using the product rule for radicals.
Step 1.1.3.8.1.1.3
Multiply by .
Step 1.1.3.8.1.1.4
Multiply by .
Step 1.1.3.8.1.2
Multiply .
Step 1.1.3.8.1.2.1
Multiply by .
Step 1.1.3.8.1.2.2
Multiply by .
Step 1.1.3.8.2
Combine the numerators over the common denominator.
Step 1.1.4
Multiply .
Step 1.1.4.1
Multiply by .
Step 1.1.4.2
Multiply by .
Step 1.1.5
Apply the distributive property.
Step 1.1.6
Combine using the product rule for radicals.
Step 1.1.7
Combine using the product rule for radicals.
Step 1.1.8
Simplify each term.
Step 1.1.8.1
Multiply by .
Step 1.1.8.2
Rewrite as .
Step 1.1.8.2.1
Factor out of .
Step 1.1.8.2.2
Rewrite as .
Step 1.1.8.3
Pull terms out from under the radical.
Step 1.1.8.4
Multiply by .
Step 1.2
To write as a fraction with a common denominator, multiply by .
Step 1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 1.3.1
Multiply by .
Step 1.3.2
Multiply by .
Step 1.4
Combine the numerators over the common denominator.
Step 1.5
Simplify the numerator.
Step 1.5.1
Apply the distributive property.
Step 1.5.2
Move to the left of .
Step 1.5.3
Multiply by .
Step 1.5.4
Add and .
Step 1.5.5
Add and .
Step 1.5.6
Add and .
Step 1.6
Cancel the common factor of and .
Step 1.6.1
Factor out of .
Step 1.6.2
Cancel the common factors.
Step 1.6.2.1
Factor out of .
Step 1.6.2.2
Cancel the common factor.
Step 1.6.2.3
Rewrite the expression.
Step 2
Divide by .
Step 3