Trigonometry Examples

Find the Exact Value cos(75)+cos(15)
Step 1
Simplify each term.
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Step 1.1
The exact value of is .
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Step 1.1.1
Split into two angles where the values of the six trigonometric functions are known.
Step 1.1.2
Apply the sum of angles identity .
Step 1.1.3
The exact value of is .
Step 1.1.4
The exact value of is .
Step 1.1.5
The exact value of is .
Step 1.1.6
The exact value of is .
Step 1.1.7
Simplify .
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Step 1.1.7.1
Simplify each term.
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Step 1.1.7.1.1
Multiply .
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Step 1.1.7.1.1.1
Multiply by .
Step 1.1.7.1.1.2
Combine using the product rule for radicals.
Step 1.1.7.1.1.3
Multiply by .
Step 1.1.7.1.1.4
Multiply by .
Step 1.1.7.1.2
Multiply .
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Step 1.1.7.1.2.1
Multiply by .
Step 1.1.7.1.2.2
Multiply by .
Step 1.1.7.2
Combine the numerators over the common denominator.
Step 1.2
The exact value of is .
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Step 1.2.1
Split into two angles where the values of the six trigonometric functions are known.
Step 1.2.2
Separate negation.
Step 1.2.3
Apply the difference of angles identity .
Step 1.2.4
The exact value of is .
Step 1.2.5
The exact value of is .
Step 1.2.6
The exact value of is .
Step 1.2.7
The exact value of is .
Step 1.2.8
Simplify .
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Step 1.2.8.1
Simplify each term.
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Step 1.2.8.1.1
Multiply .
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Step 1.2.8.1.1.1
Multiply by .
Step 1.2.8.1.1.2
Combine using the product rule for radicals.
Step 1.2.8.1.1.3
Multiply by .
Step 1.2.8.1.1.4
Multiply by .
Step 1.2.8.1.2
Multiply .
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Step 1.2.8.1.2.1
Multiply by .
Step 1.2.8.1.2.2
Multiply by .
Step 1.2.8.2
Combine the numerators over the common denominator.
Step 2
Simplify terms.
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Step 2.1
Combine the numerators over the common denominator.
Step 2.2
Add and .
Step 2.3
Add and .
Step 2.4
Add and .
Step 2.5
Cancel the common factor of and .
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Step 2.5.1
Factor out of .
Step 2.5.2
Cancel the common factors.
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Step 2.5.2.1
Factor out of .
Step 2.5.2.2
Cancel the common factor.
Step 2.5.2.3
Rewrite the expression.
Step 3
The result can be shown in multiple forms.
Exact Form:
Decimal Form: