Trigonometry Examples

Solve for x cos(x)^2csc(x)sec(x)=cot(x)
Step 1
Simplify the left side.
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Step 1.1
Simplify .
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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 1.1.4
Combine.
Step 1.1.5
Cancel the common factor of and .
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Step 1.1.5.1
Factor out of .
Step 1.1.5.2
Cancel the common factors.
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Step 1.1.5.2.1
Factor out of .
Step 1.1.5.2.2
Cancel the common factor.
Step 1.1.5.2.3
Rewrite the expression.
Step 1.1.6
Multiply by .
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
Cancel the common factor of .
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Step 4.1
Cancel the common factor.
Step 4.2
Rewrite the expression.
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
For the two functions to be equal, the arguments of each must be equal.
Step 7
Move all terms containing to the left side of the equation.
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Step 7.1
Subtract from both sides of the equation.
Step 7.2
Subtract from .
Step 8
Since , the equation will always be true for any value of .
All real numbers
Step 9
The result can be shown in multiple forms.
All real numbers
Interval Notation: