Trigonometry Examples

Verify the Identity (cos(x))/(1-sin(x))=sec(x)+tan(x)
Step 1
Start on the left side.
Step 2
Multiply by .
Step 3
Combine.
Step 4
Simplify numerator.
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Step 4.1
Apply the distributive property.
Step 4.2
Multiply by .
Step 5
Simplify denominator.
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Step 5.1
Expand using the FOIL Method.
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Step 5.1.1
Apply the distributive property.
Step 5.1.2
Apply the distributive property.
Step 5.1.3
Apply the distributive property.
Step 5.2
Simplify and combine like terms.
Step 6
Apply pythagorean identity.
Step 7
Simplify.
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Step 7.1
Factor out of .
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Step 7.1.1
Multiply by .
Step 7.1.2
Factor out of .
Step 7.1.3
Factor out of .
Step 7.2
Cancel the common factors.
Step 8
Now consider the right side of the equation.
Step 9
Convert to sines and cosines.
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Step 9.1
Apply the reciprocal identity to .
Step 9.2
Write in sines and cosines using the quotient identity.
Step 10
Combine the numerators over the common denominator.
Step 11
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity