Come dimostrate #tanx + cotx = secx cscx #?

Dato:
#tan x+ cot x= sec x *cscx#

Inizia dal lato destro, modificalo in #sinx# ; #cosx#

#sinx/cosx + cosx/sinx = sec x *csc x#

#color(red)([sinx/sinx])*(sinx/cosx)# + #color(blue)
[cosx/cosx]*cosx/sinx# = #sec x*cscx#

#[sin^2x+cos^2x]/(sinx*cosx) = sec x *cscx#

#1/(sinx *cos x) = sec x *csc x#

#(1/sinx)(1/cosx) = secx*cscx#

#sec x *csc x = secx *csc x#

Dimostrazione completata!

*#sin^2x + cos^2x= 1#

*#1/sinx = csc x# ; #1/cosx = secx#