Trigonometry Examples

Verify the Identity 1/(cos(x))-(cos(x))/(1+sin(x))=tan(x)
Step 1
Start on the left side.
Step 2
Simplify the expression.
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Step 2.1
To write as a fraction with a common denominator, multiply by .
Step 2.2
To write as a fraction with a common denominator, multiply by .
Step 2.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 2.3.1
Multiply by .
Step 2.3.2
Multiply by .
Step 2.3.3
Reorder the factors of .
Step 2.4
Combine the numerators over the common denominator.
Step 2.5
Simplify the numerator.
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Step 2.5.1
Multiply .
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Step 2.5.1.1
Raise to the power of .
Step 2.5.1.2
Raise to the power of .
Step 2.5.1.3
Use the power rule to combine exponents.
Step 2.5.1.4
Add and .
Step 2.5.2
Move .
Step 2.5.3
Apply pythagorean identity.
Step 2.5.4
Factor out of .
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Step 2.5.4.1
Factor out of .
Step 2.5.4.2
Multiply by .
Step 2.5.4.3
Factor out of .
Step 2.6
Cancel the common factor of and .
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Step 2.6.1
Reorder terms.
Step 2.6.2
Cancel the common factor.
Step 2.6.3
Rewrite the expression.
Step 3
Rewrite as .
Step 4
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity