Trigonometry Examples

Rationalize the Denominator ((8cos(x))^2)/( square root of 64-x^2)
Step 1
Simplify the numerator.
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Step 1.1
Apply the product rule to .
Step 1.2
Raise to the power of .
Step 2
Simplify the denominator.
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Step 2.1
Rewrite as .
Step 2.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 3
Multiply by .
Step 4
Combine and simplify the denominator.
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Step 4.1
Multiply by .
Step 4.2
Raise to the power of .
Step 4.3
Raise to the power of .
Step 4.4
Use the power rule to combine exponents.
Step 4.5
Add and .
Step 4.6
Rewrite as .
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Step 4.6.1
Use to rewrite as .
Step 4.6.2
Apply the power rule and multiply exponents, .
Step 4.6.3
Combine and .
Step 4.6.4
Cancel the common factor of .
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Step 4.6.4.1
Cancel the common factor.
Step 4.6.4.2
Rewrite the expression.
Step 4.6.5
Simplify.