Trigonometry Examples

Simplify (tan(x)^3(x)-sec(x)^2xtan(x))/(cot(-x))
Step 1
Simplify the numerator.
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Step 1.1
Factor out of .
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Step 1.1.1
Factor out of .
Step 1.1.2
Factor out of .
Step 1.1.3
Factor out of .
Step 1.2
Reorder and .
Step 1.3
Factor out of .
Step 1.4
Factor out of .
Step 1.5
Factor out of .
Step 1.6
Apply pythagorean identity.
Step 1.7
Combine exponents.
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Step 1.7.1
Factor out negative.
Step 1.7.2
Multiply by .
Step 2
Since is an odd function, rewrite as .
Step 3
Dividing two negative values results in a positive value.
Step 4
Separate fractions.
Step 5
Rewrite in terms of sines and cosines.
Step 6
Rewrite in terms of sines and cosines.
Step 7
Multiply by the reciprocal of the fraction to divide by .
Step 8
Simplify.
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Step 8.1
Convert from to .
Step 8.2
Convert from to .
Step 8.3
Raise to the power of .
Step 8.4
Raise to the power of .
Step 8.5
Use the power rule to combine exponents.
Step 8.6
Add and .
Step 9
Divide by .