Trigonometry Examples

Solve for ? (sec(x))/(cos(x))-(tan(x))/(cot(x))=1
Step 1
Simplify the left side.
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Step 1.1
Simplify .
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Step 1.1.1
Simplify terms.
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Step 1.1.1.1
Simplify each term.
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Step 1.1.1.1.1
Rewrite in terms of sines and cosines.
Step 1.1.1.1.2
Rewrite as a product.
Step 1.1.1.1.3
Multiply by .
Step 1.1.1.1.4
Simplify the denominator.
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Step 1.1.1.1.4.1
Raise to the power of .
Step 1.1.1.1.4.2
Raise to the power of .
Step 1.1.1.1.4.3
Use the power rule to combine exponents.
Step 1.1.1.1.4.4
Add and .
Step 1.1.1.1.5
Rewrite in terms of sines and cosines.
Step 1.1.1.1.6
Rewrite in terms of sines and cosines.
Step 1.1.1.1.7
Multiply by the reciprocal of the fraction to divide by .
Step 1.1.1.1.8
Multiply by .
Step 1.1.1.1.9
Simplify the numerator.
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Step 1.1.1.1.9.1
Raise to the power of .
Step 1.1.1.1.9.2
Raise to the power of .
Step 1.1.1.1.9.3
Use the power rule to combine exponents.
Step 1.1.1.1.9.4
Add and .
Step 1.1.1.1.10
Simplify the denominator.
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Step 1.1.1.1.10.1
Raise to the power of .
Step 1.1.1.1.10.2
Raise to the power of .
Step 1.1.1.1.10.3
Use the power rule to combine exponents.
Step 1.1.1.1.10.4
Add and .
Step 1.1.1.2
Combine the numerators over the common denominator.
Step 1.1.2
Apply pythagorean identity.
Step 1.1.3
Cancel the common factor of .
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Step 1.1.3.1
Cancel the common factor.
Step 1.1.3.2
Rewrite the expression.
Step 2
Since , the equation will always be true for any value of .
All real numbers
Step 3
The result can be shown in multiple forms.
All real numbers
Interval Notation: