tan(pie/2-x) cot x / csc^2(-x)-1

Question

use the fundamental identities to simplify the expression

Answer 1

Please recall:

tan (pi/2 - x) = cot (x)

csc (-x) = -csc (x)

 

So, subtituting them into the equation:

cot(x) . cot(x) /(((-csc(x))^2 - 1)

which can be simplify to

(cot(x))^2/(((csc(x))^2 - 1)

 

Also, recall that 1 + (cot(x))^2 = (csc(x))^2

So after subtituting the denominator

(cot(x))^2/(cot(x))^2 = 1