Trigonometry Examples

Evaluate v(((5 square root of 2)/2)^2+(-(5 square root of 2)/2)^2)
Step 1
Simplify each term.
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Step 1.1
Use the power rule to distribute the exponent.
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Step 1.1.1
Apply the product rule to .
Step 1.1.2
Apply the product rule to .
Step 1.2
Simplify the numerator.
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Step 1.2.1
Raise to the power of .
Step 1.2.2
Rewrite as .
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Step 1.2.2.1
Use to rewrite as .
Step 1.2.2.2
Apply the power rule and multiply exponents, .
Step 1.2.2.3
Combine and .
Step 1.2.2.4
Cancel the common factor of .
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Step 1.2.2.4.1
Cancel the common factor.
Step 1.2.2.4.2
Rewrite the expression.
Step 1.2.2.5
Evaluate the exponent.
Step 1.3
Raise to the power of .
Step 1.4
Multiply by .
Step 1.5
Cancel the common factor of and .
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Step 1.5.1
Factor out of .
Step 1.5.2
Cancel the common factors.
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Step 1.5.2.1
Factor out of .
Step 1.5.2.2
Cancel the common factor.
Step 1.5.2.3
Rewrite the expression.
Step 1.6
Use the power rule to distribute the exponent.
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Step 1.6.1
Apply the product rule to .
Step 1.6.2
Apply the product rule to .
Step 1.6.3
Apply the product rule to .
Step 1.7
Raise to the power of .
Step 1.8
Multiply by .
Step 1.9
Simplify the numerator.
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Step 1.9.1
Raise to the power of .
Step 1.9.2
Rewrite as .
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Step 1.9.2.1
Use to rewrite as .
Step 1.9.2.2
Apply the power rule and multiply exponents, .
Step 1.9.2.3
Combine and .
Step 1.9.2.4
Cancel the common factor of .
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Step 1.9.2.4.1
Cancel the common factor.
Step 1.9.2.4.2
Rewrite the expression.
Step 1.9.2.5
Evaluate the exponent.
Step 1.10
Raise to the power of .
Step 1.11
Multiply by .
Step 1.12
Cancel the common factor of and .
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Step 1.12.1
Factor out of .
Step 1.12.2
Cancel the common factors.
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Step 1.12.2.1
Factor out of .
Step 1.12.2.2
Cancel the common factor.
Step 1.12.2.3
Rewrite the expression.
Step 2
Combine fractions.
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Step 2.1
Combine the numerators over the common denominator.
Step 2.2
Simplify the expression.
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Step 2.2.1
Add and .
Step 2.2.2
Divide by .
Step 2.2.3
Move to the left of .