Trigonometry Examples

Solve for ? sin(x)(tan(x)+cot(x))=sec(x)
Step 1
Simplify the left side.
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Step 1.1
Simplify .
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Step 1.1.1
Simplify each term.
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Step 1.1.1.1
Rewrite in terms of sines and cosines.
Step 1.1.1.2
Rewrite in terms of sines and cosines.
Step 1.1.2
Apply the distributive property.
Step 1.1.3
Multiply .
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Step 1.1.3.1
Combine and .
Step 1.1.3.2
Raise to the power of .
Step 1.1.3.3
Raise to the power of .
Step 1.1.3.4
Use the power rule to combine exponents.
Step 1.1.3.5
Add and .
Step 1.1.4
Cancel the common factor of .
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Step 1.1.4.1
Cancel the common factor.
Step 1.1.4.2
Rewrite the expression.
Step 2
Simplify the right side.
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Step 2.1
Rewrite in terms of sines and cosines.
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
Raise to the power of .
Step 6.2
Raise to the power of .
Step 6.3
Use the power rule to combine exponents.
Step 6.4
Add and .
Step 7
Apply pythagorean identity.
Step 8
Cancel the common factor of .
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Step 8.1
Cancel the common factor.
Step 8.2
Rewrite the expression.
Step 9
Since , the equation will always be true for any value of .
All real numbers
Step 10
The result can be shown in multiple forms.
All real numbers
Interval Notation: