trig identity?

Question

Prove one trig identity please?
steps please
(csc(-x) +1) / cos(-x) + cot (-x) = sec x

Answer 1

The right identity is : (csc(-x) +1) / (cos(-x) + cot (-x)) = sec x
Rem. : csc(-x) = - csc(x), cos(-x)=cos(x), cot(-x)= - cot(x),
csc(x) = 1/sin(x), cot(x)= cos(x)/sin(x)
L. H. S. = (- csc(x) + 1)/(cos(x) - cos(x)/sin(x))
.............= (- 1/sin(x) + 1)/(cos(x) - cos(x)/sin(x))
.............= (- 1 + sin(x))/(cos(x) sin(x) - cos(x))
.............= ( -1 + sin(x)) / [cos(x) ( sin(x) -1)]
............ = 1/ cos(x) = sec(x) = R.H.S. (q. e. d.)

Answer 2

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