Question

what is the value of tan(45+x)–cot(45–x)

Answer 1

By complementary ratios, we have
tan(45+A) - tan(90 - [45-A])       {cotA = tan(90-A)}
tan(45+A) - tan(90-45+A)
tan(45+A) - tan(45+A)
= 0

Answer 2

Well you can write

$\tan(45 + x) = \tan(90 - (45 - x)$
Which gives us
$\cot(45 - x)$

Therefore,
$\cot(45 - x) - \cot(45 - x) = 0$
Hope it helps

Yours Truly
Yumieo