Trigonometry Examples

Verify the Identity (tan(theta)+cot(theta))sin(theta)=sec(theta)
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 2.2
Apply the distributive property.
Step 2.3
Multiply .
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Step 2.3.1
Combine and .
Step 2.3.2
Raise to the power of .
Step 2.3.3
Raise to the power of .
Step 2.3.4
Use the power rule to combine exponents.
Step 2.3.5
Add and .
Step 2.4
Cancel the common factor of .
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Step 2.4.1
Cancel the common factor.
Step 2.4.2
Rewrite the expression.
Step 3
Apply Pythagorean identity in reverse.
Step 4
Simplify.
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Step 4.1
Simplify the numerator.
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Step 4.1.1
Rewrite as .
Step 4.1.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 4.2
To write as a fraction with a common denominator, multiply by .
Step 4.3
Combine the numerators over the common denominator.
Step 4.4
Simplify the numerator.
Step 5
Rewrite as .
Step 6
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity