Trigonometry Examples

Simplify (cot(x)+tan(x))^2-(cot(x)-tan(x))^2
Step 1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2
Simplify terms.
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Step 2.1
Combine the opposite terms in .
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Step 2.1.1
Subtract from .
Step 2.1.2
Add and .
Step 2.2
Add and .
Step 2.3
Simplify each term.
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Step 2.3.1
Apply the distributive property.
Step 2.3.2
Multiply .
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Step 2.3.2.1
Multiply by .
Step 2.3.2.2
Multiply by .
Step 2.4
Simplify by adding terms.
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Step 2.4.1
Combine the opposite terms in .
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Step 2.4.1.1
Subtract from .
Step 2.4.1.2
Add and .
Step 2.4.2
Add and .
Step 3
Rewrite in terms of sines and cosines, then cancel the common factors.
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Step 3.1
Add parentheses.
Step 3.2
Reorder and .
Step 3.3
Add parentheses.
Step 3.4
Reorder and .
Step 3.5
Rewrite in terms of sines and cosines.
Step 3.6
Cancel the common factors.
Step 4
Multiply .
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Step 4.1
Multiply by .
Step 4.2
Multiply by .