Proving trigonometry function?

Question

prove that tan(x)+cot(x)=sec(x)*csc(x)

please show working out

Answer 1

tan x + cot x

= sin x / cos x + cos x / sin x

= (sin² x + cos² x) / sin x cos x

= 1 / cos x sins x

= sec x csc x .

Answer 2

sinx/cosx + cosx/sinx

=(sin^2 x + cos62 x)/(cosx sinx)

=1/(cosx sinx)

=1/cosx * 1/sinx

=secx cscx

Answer 3

tanx=sinx/cosx    cotx=cosx/sinx   secx=1/cosx    cscx=1/sinx

tan(x)+cot(x)= 1/cosx*1/sinx

tan(x)+cot(x)= 1/cos(x)sin(x)

tan(x)+cot(x)=tan(x)+cot(x)

Answer 4

sinx/cosx + cosx/sinx =

(sin²x + cos²x) / sinx*cosx =

1 / sinx*cosx = secx*cscx

Good luck.