Question

Simplify the expression tan(-x)csc(-x)/sec(-x)cot(-x)

Answer 1

The answer is csc(x)cot(x)tan(x) over sec(x)

Answer 2

`( tan(-x) cosec (-x))/(sec (-x) cot (-x))` ≡
`( [- tan(x)] [-cosec (-x)])/([sec (x)] [-cot (x)])`

≡
`( tan(x) cosec (-x))/(-sec (x) cot (x))`

≡
`( ((sin (x))/(cos (x))) ((1)/(sin (x ))) )/((- (1)/(cos (x))) ( (cos (x))/(sin (x))) )`

≡
`( (1)/(cos (x)) )/(- (1)/(sin (x)) )`

≡
`- (sin (x))/(cos (x))`

≡
`- tan (x)`

⇒
`( tan(-x) cosec (-x))/(sec (-x) cot (-x))` ≡
`tan (-x)`