Precalculus Examples

Verify the Identity (tan(x)-sin(-x))/(1+cos(x))=tan(x)
Step 1
Start on the left side.
Step 2
Since is an odd function, rewrite as .
Step 3
Write in sines and cosines using the quotient identity.
Step 4
Simplify.
Tap for more steps...
Step 4.1
Multiply the numerator and denominator of the fraction by .
Tap for more steps...
Step 4.1.1
Multiply by .
Step 4.1.2
Combine.
Step 4.2
Apply the distributive property.
Step 4.3
Cancel the common factor of .
Tap for more steps...
Step 4.3.1
Cancel the common factor.
Step 4.3.2
Rewrite the expression.
Step 4.4
Simplify the numerator.
Tap for more steps...
Step 4.4.1
Factor out of .
Tap for more steps...
Step 4.4.1.1
Multiply by .
Step 4.4.1.2
Factor out of .
Step 4.4.1.3
Factor out of .
Step 4.4.2
Multiply by .
Step 4.4.3
Multiply by .
Step 4.5
Factor out of .
Tap for more steps...
Step 4.5.1
Factor out of .
Step 4.5.2
Factor out of .
Step 4.5.3
Factor out of .
Step 4.6
Cancel the common factor of .
Step 5
Rewrite as .
Step 6
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity