Answer:
The answer is cot(x)
Step-by-step explanation:
Greetings !
[tex] \tan(x) \csc {}^{2} (x) - \tan(x) [/tex]
Rewrite using trig identity
[tex] - \tan(x) + \csc {}^{2} (x) \tan(x) [/tex]
use the Pythagorean idea
[tex] \csc {}^{2} (x) = 1 + \cot {}^{2} (x) [/tex]
[tex] - \tan(x) + (1 + \cot {}^{2} (x)) \tan(x) [/tex]
simplify
[tex] \cot {}^{2} (x) \tan(x) [/tex]
use basic trigonometric identity
[tex] \tan(x ) = \frac{1}{ \cot(x) } [/tex]
simplify
[tex] \cot {}^{2} (x) \frac{1}{ \cot(x) } [/tex]
gives you
[tex] \cot(x) [/tex]
Hope it helps!
