[tex] \frac{ tan(-x) cosec (-x)}{sec (-x) cot (-x)} [/tex] ≡ [tex]\frac{ [- tan(x)] [-cosec (-x)]}{[sec (x)] [-cot (x)]}[/tex]
≡ [tex]\frac{ tan(x) cosec (-x)}{-sec (x) cot (x)}[/tex]
≡ [tex] \frac{ (\frac{sin (x)}{cos (x)}) (\frac{1}{sin (x )}) }{(- \frac{1}{cos (x)}) ( \frac{cos (x)}{sin (x)}) } [/tex]
≡ [tex] \frac{ \frac{1}{cos (x)} }{- \frac{1}{sin (x)} } [/tex]
≡ [tex] - \frac{sin (x)}{cos (x)} [/tex]
≡ [tex]- tan (x)[/tex]
⇒ [tex] \frac{ tan(-x) cosec (-x)}{sec (-x) cot (-x)} [/tex] ≡ [tex]tan (-x)[/tex]
