Trigonometry Examples

Simplify (cos(t)-1)/(sec(t)-1)
Step 1
Rewrite in terms of sines and cosines.
Step 2
Multiply the numerator and denominator of the fraction by .
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Step 2.1
Multiply by .
Step 2.2
Combine.
Step 3
Apply the distributive property.
Step 4
Cancel the common factor of .
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Step 4.1
Cancel the common factor.
Step 4.2
Rewrite the expression.
Step 5
Simplify the numerator.
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Step 5.1
Multiply .
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Step 5.1.1
Raise to the power of .
Step 5.1.2
Raise to the power of .
Step 5.1.3
Use the power rule to combine exponents.
Step 5.1.4
Add and .
Step 5.2
Move to the left of .
Step 5.3
Rewrite as .
Step 5.4
Factor out of .
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Step 5.4.1
Factor out of .
Step 5.4.2
Factor out of .
Step 5.4.3
Factor out of .
Step 6
Simplify the denominator.
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Step 6.1
Move to the left of .
Step 6.2
Rewrite as .
Step 7
Reduce the expression by cancelling the common factors.
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Step 7.1
Cancel the common factor of and .
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Step 7.1.1
Factor out of .
Step 7.1.2
Rewrite as .
Step 7.1.3
Factor out of .
Step 7.1.4
Reorder terms.
Step 7.1.5
Cancel the common factor.
Step 7.1.6
Divide by .
Step 7.2
Simplify the expression.
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Step 7.2.1
Move to the left of .
Step 7.2.2
Rewrite as .