Let's first subtract the two expressions. Use the butterfly method to subtract. The steps are:
1. Multiply the numerator of the first term by the denominator of the second term.
[tex](tanx)\times(tanx)=tan^2x[/tex]
2. Multiply the numerator of the second term by the denominator of the first term.
[tex]1\times sec^2x=sec^2x[/tex]
3. Subtract the results in steps 1 and 2.
[tex]tan^2x-sec^2x[/tex]
4. Divide step 3 by the product of the two denominators.
[tex]\frac{tan^2x-sec^2x}{tanx}[/tex]
We have finished subtracting the two terms. Let's now simplify the difference.
Recall that one of the Pythagorean identities is 1 + tan²x = sec²x. This identity can also be written as tan²x - sec²x = -1.
Since tan²x - sec²x = -1, the numerator of the difference is just equal to -1. The expression then becomes:
[tex]\frac{-1}{tanx}\text{ }or\text{ }just-\frac{1}{tanx}[/tex]
ANSWER:
The answer is -1/tan x.
