Trigonometry Examples

Verify the Identity (sec(x))/(1-tan(x))=1/(cos(x)-sin(x))
Step 1
Start on the left side.
Step 2
Convert to sines and cosines.
Tap for more steps...
Step 2.1
Apply the reciprocal identity to .
Step 2.2
Write in sines and cosines using the quotient identity.
Step 3
Simplify.
Tap for more steps...
Step 3.1
Multiply the numerator by the reciprocal of the denominator.
Step 3.2
Simplify the denominator.
Tap for more steps...
Step 3.2.1
Write as a fraction with a common denominator.
Step 3.2.2
Combine the numerators over the common denominator.
Step 3.3
Multiply the numerator by the reciprocal of the denominator.
Step 3.4
Multiply by .
Step 3.5
Cancel the common factor of .
Step 4
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity