Finite Math Examples

Solve for x (cos(x))/(1-sin(x))-(sin(x))/(cos(x))=sec(x)
Step 1
Simplify the left side.
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Step 1.1
Simplify .
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Step 1.1.1
To write as a fraction with a common denominator, multiply by .
Step 1.1.2
To write as a fraction with a common denominator, multiply by .
Step 1.1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 1.1.3.1
Multiply by .
Step 1.1.3.2
Multiply by .
Step 1.1.3.3
Reorder the factors of .
Step 1.1.4
Combine the numerators over the common denominator.
Step 1.1.5
Simplify the numerator.
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Step 1.1.5.1
Multiply .
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Step 1.1.5.1.1
Raise to the power of .
Step 1.1.5.1.2
Raise to the power of .
Step 1.1.5.1.3
Use the power rule to combine exponents.
Step 1.1.5.1.4
Add and .
Step 1.1.5.2
Apply the distributive property.
Step 1.1.5.3
Multiply by .
Step 1.1.5.4
Multiply .
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Step 1.1.5.4.1
Multiply by .
Step 1.1.5.4.2
Multiply by .
Step 1.1.5.4.3
Raise to the power of .
Step 1.1.5.4.4
Raise to the power of .
Step 1.1.5.4.5
Use the power rule to combine exponents.
Step 1.1.5.4.6
Add and .
Step 1.1.5.5
Rewrite in a factored form.
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Step 1.1.5.5.1
Rearrange terms.
Step 1.1.5.5.2
Rearrange terms.
Step 1.1.5.5.3
Apply pythagorean identity.
Step 1.1.6
Cancel the common factor of and .
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Step 1.1.6.1
Reorder terms.
Step 1.1.6.2
Cancel the common factor.
Step 1.1.6.3
Rewrite the expression.
Step 2
Simplify the right side.
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Step 2.1
Rewrite in terms of sines and cosines.
Step 3
Multiply both sides of the equation by .
Step 4
Cancel the common factor of .
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Step 4.1
Cancel the common factor.
Step 4.2
Rewrite the expression.
Step 5
Cancel the common factor of .
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Step 5.1
Cancel the common factor.
Step 5.2
Rewrite the expression.
Step 6
Since , the equation will always be true for any value of .
All real numbers
Step 7
The result can be shown in multiple forms.
All real numbers
Interval Notation: