Trigonometry Examples

Solve for x csc(x)-cot(x)=1/(csc(x)+cot(x))
Step 1
Multiply both sides by .
Step 2
Simplify.
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Step 2.1
Simplify the left side.
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Step 2.1.1
Simplify .
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Step 2.1.1.1
Expand using the FOIL Method.
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Step 2.1.1.1.1
Apply the distributive property.
Step 2.1.1.1.2
Apply the distributive property.
Step 2.1.1.1.3
Apply the distributive property.
Step 2.1.1.2
Simplify terms.
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Step 2.1.1.2.1
Combine the opposite terms in .
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Step 2.1.1.2.1.1
Reorder the factors in the terms and .
Step 2.1.1.2.1.2
Subtract from .
Step 2.1.1.2.1.3
Add and .
Step 2.1.1.2.2
Simplify each term.
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Step 2.1.1.2.2.1
Multiply .
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Step 2.1.1.2.2.1.1
Raise to the power of .
Step 2.1.1.2.2.1.2
Raise to the power of .
Step 2.1.1.2.2.1.3
Use the power rule to combine exponents.
Step 2.1.1.2.2.1.4
Add and .
Step 2.1.1.2.2.2
Multiply .
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Step 2.1.1.2.2.2.1
Raise to the power of .
Step 2.1.1.2.2.2.2
Raise to the power of .
Step 2.1.1.2.2.2.3
Use the power rule to combine exponents.
Step 2.1.1.2.2.2.4
Add and .
Step 2.1.1.3
Apply pythagorean identity.
Step 2.2
Simplify the right side.
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Step 2.2.1
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Rewrite the expression.
Step 3
Since , the equation will always be true for any value of .
All real numbers
Step 4
The result can be shown in multiple forms.
All real numbers
Interval Notation: