Trigonometry Examples

Evaluate square root of (1-( square root of 2)/2)/(1+( square root of 2)/2)
Step 1
Write as a fraction with a common denominator.
Step 2
Combine the numerators over the common denominator.
Step 3
Write as a fraction with a common denominator.
Step 4
Combine the numerators over the common denominator.
Step 5
Multiply the numerator by the reciprocal of the denominator.
Step 6
Cancel the common factor of .
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Step 6.1
Cancel the common factor.
Step 6.2
Rewrite the expression.
Step 7
Multiply by .
Step 8
Multiply by .
Step 9
Expand the denominator using the FOIL method.
Step 10
Simplify.
Step 11
Apply the distributive property.
Step 12
Cancel the common factor of .
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Step 12.1
Cancel the common factor.
Step 12.2
Rewrite the expression.
Step 13
Combine and .
Step 14
Find the common denominator.
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Step 14.1
Write as a fraction with denominator .
Step 14.2
Multiply by .
Step 14.3
Multiply by .
Step 14.4
Write as a fraction with denominator .
Step 14.5
Multiply by .
Step 14.6
Multiply by .
Step 15
Combine the numerators over the common denominator.
Step 16
Simplify each term.
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Step 16.1
Multiply by .
Step 16.2
Multiply by .
Step 16.3
Apply the distributive property.
Step 16.4
Multiply by .
Step 16.5
Multiply .
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Step 16.5.1
Multiply by .
Step 16.5.2
Multiply by .
Step 16.6
Apply the distributive property.
Step 16.7
Combine using the product rule for radicals.
Step 16.8
Simplify each term.
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Step 16.8.1
Multiply by .
Step 16.8.2
Rewrite as .
Step 16.8.3
Pull terms out from under the radical, assuming positive real numbers.
Step 17
Simplify terms.
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Step 17.1
Add and .
Step 17.2
Subtract from .
Step 17.3
Cancel the common factor of and .
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Step 17.3.1
Factor out of .
Step 17.3.2
Factor out of .
Step 17.3.3
Factor out of .
Step 17.3.4
Cancel the common factors.
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Step 17.3.4.1
Factor out of .
Step 17.3.4.2
Cancel the common factor.
Step 17.3.4.3
Rewrite the expression.
Step 17.3.4.4
Divide by .
Step 18
The result can be shown in multiple forms.
Exact Form:
Decimal Form: