Trigonometry Examples

Solve for x 2csc(2x)-cot(x)=tan(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
Combine and .
Step 1.1.3
Rewrite in terms of sines and cosines.
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
Rewrite using the commutative property of multiplication.
Step 7
Simplify each term.
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Step 7.1
Combine and .
Step 7.2
Simplify the numerator.
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Step 7.2.1
Apply the sine double-angle identity.
Step 7.2.2
Combine exponents.
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Step 7.2.2.1
Raise to the power of .
Step 7.2.2.2
Raise to the power of .
Step 7.2.2.3
Use the power rule to combine exponents.
Step 7.2.2.4
Add and .
Step 7.3
Cancel the common factor of .
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Step 7.3.1
Cancel the common factor.
Step 7.3.2
Divide by .
Step 7.4
Multiply by .
Step 8
Factor out of .
Step 9
Factor out of .
Step 10
Factor out of .
Step 11
Apply pythagorean identity.
Step 12
Combine and .
Step 13
Simplify the numerator.
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Step 13.1
Apply the sine double-angle identity.
Step 13.2
Combine exponents.
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Step 13.2.1
Raise to the power of .
Step 13.2.2
Raise to the power of .
Step 13.2.3
Use the power rule to combine exponents.
Step 13.2.4
Add and .
Step 14
Cancel the common factor of .
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Step 14.1
Cancel the common factor.
Step 14.2
Divide by .
Step 15
Move all terms containing to the left side of the equation.
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Step 15.1
Subtract from both sides of the equation.
Step 15.2
Subtract from .
Step 16
Since , the equation will always be true for any value of .
All real numbers
Step 17
The result can be shown in multiple forms.
All real numbers
Interval Notation: