Trigonometry Examples

Solve for ? tan(x)+cot(x)=csc(x)sec(x)
Step 1
Simplify the left side.
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Step 1.1
Simplify each term.
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Step 1.1.1
Rewrite in terms of sines and cosines.
Step 1.1.2
Rewrite in terms of sines and cosines.
Step 2
Simplify the right side.
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Step 2.1
Simplify .
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Step 2.1.1
Rewrite in terms of sines and cosines.
Step 2.1.2
Rewrite in terms of sines and cosines.
Step 2.1.3
Multiply by .
Step 3
Multiply both sides of the equation by .
Step 4
Apply the distributive property.
Step 5
Cancel the common factor of .
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Step 5.1
Cancel the common factor.
Step 5.2
Rewrite the expression.
Step 6
Multiply .
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Step 6.1
Combine and .
Step 6.2
Raise to the power of .
Step 6.3
Raise to the power of .
Step 6.4
Use the power rule to combine exponents.
Step 6.5
Add and .
Step 7
Cancel the common factor of .
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Step 7.1
Factor out of .
Step 7.2
Cancel the common factor.
Step 7.3
Rewrite the expression.
Step 8
Subtract from both sides of the equation.
Step 9
Simplify .
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Step 9.1
Combine the numerators over the common denominator.
Step 9.2
Reorder and .
Step 9.3
Rewrite as .
Step 9.4
Factor out of .
Step 9.5
Factor out of .
Step 9.6
Rewrite as .
Step 9.7
Apply pythagorean identity.
Step 9.8
Cancel the common factor of and .
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Step 9.8.1
Factor out of .
Step 9.8.2
Cancel the common factors.
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Step 9.8.2.1
Multiply by .
Step 9.8.2.2
Cancel the common factor.
Step 9.8.2.3
Rewrite the expression.
Step 9.8.2.4
Divide by .
Step 9.9
Subtract from .
Step 10
Since , the equation will always be true for any value of .
All real numbers
Step 11
The result can be shown in multiple forms.
All real numbers
Interval Notation: