Trigonometry Examples

Verify the Identity sec(x)-tan(x)sin(x)=1/(sec(x))
Step 1
Start on the left side.
Step 2
Simplify the expression.
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Step 2.1
Simplify each term.
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Step 2.1.1
Rewrite in terms of sines and cosines.
Step 2.1.2
Rewrite in terms of sines and cosines.
Step 2.1.3
Multiply .
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Step 2.1.3.1
Combine and .
Step 2.1.3.2
Raise to the power of .
Step 2.1.3.3
Raise to the power of .
Step 2.1.3.4
Use the power rule to combine exponents.
Step 2.1.3.5
Add and .
Step 2.2
Combine the numerators over the common denominator.
Step 2.3
Apply pythagorean identity.
Step 2.4
Cancel the common factor of and .
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Step 2.4.1
Factor out of .
Step 2.4.2
Cancel the common factors.
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Step 2.4.2.1
Multiply by .
Step 2.4.2.2
Cancel the common factor.
Step 2.4.2.3
Rewrite the expression.
Step 2.4.2.4
Divide by .
Step 3
Rewrite as .
Step 4
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity