Trigonometry Examples

Solve for x csc(2x)=(csc(x))/(2cos(x))
Step 1
Simplify the left side.
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Step 1.1
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
Separate fractions.
Step 2.1.2
Rewrite in terms of sines and cosines.
Step 2.1.3
Rewrite as a product.
Step 2.1.4
Multiply by .
Step 2.1.5
Multiply by .
Step 3
Multiply both sides of the equation by .
Step 4
Cancel the common factor of .
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Step 4.1
Cancel the common factor.
Step 4.2
Rewrite the expression.
Step 5
Combine and .
Step 6
Apply the sine double-angle identity.
Step 7
Cancel the common factor of .
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Step 7.1
Cancel the common factor.
Step 7.2
Rewrite the expression.
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
Cancel the common factor of .
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Step 9.1
Cancel the common factor.
Step 9.2
Rewrite the expression.
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: