Prove the following identity: tanx+cotx=(secx)(cscx)

Thxs

tanx = sinx/cosx
cotx = cosx/sinx

so...........

tanx + cotx = (secx)(cscx)

sinx/cosx + cosx/sinx

Find the LCM, which in this case is sinxcosx..........

(sin²x + cos²x) / (sinxcosx) = (secx)(cscx)

sin²x + cos²x = 1

1/sinxcosx = (secx)(cscx)

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

(secx)(cscx) = (secx)(cscx)