Trigonometry Examples

Find the Inverse (sec(x))/(csc(x))
Step 1
Interchange the variables.
Step 2
Solve for .
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Step 2.1
Rewrite the equation as .
Step 2.2
Simplify the left side.
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Step 2.2.1
Simplify .
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Step 2.2.1.1
Rewrite in terms of sines and cosines.
Step 2.2.1.2
Rewrite in terms of sines and cosines.
Step 2.2.1.3
Multiply by the reciprocal of the fraction to divide by .
Step 2.2.1.4
Convert from to .
Step 2.3
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Step 3
Replace with to show the final answer.
Step 4
Verify if is the inverse of .
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Step 4.1
To verify the inverse, check if and .
Step 4.2
Evaluate .
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Step 4.2.1
Set up the composite result function.
Step 4.2.2
Evaluate by substituting in the value of into .
Step 4.2.3
Rewrite in terms of sines and cosines.
Step 4.2.4
Rewrite in terms of sines and cosines.
Step 4.2.5
Multiply by the reciprocal of the fraction to divide by .
Step 4.2.6
Convert from to .
Step 4.3
Evaluate .
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Step 4.3.1
Set up the composite result function.
Step 4.3.2
Evaluate by substituting in the value of into .
Step 4.3.3
Rewrite in terms of sines and cosines.
Step 4.3.4
Rewrite in terms of sines and cosines.
Step 4.3.5
Multiply by the reciprocal of the fraction to divide by .
Step 4.3.6
Convert from to .
Step 4.3.7
The functions tangent and arctangent are inverses.
Step 4.4
Since and , then is the inverse of .