I do not see why you changed the + into a ÷, namely:
sin x cos x
----- + ----- =
sin x sin x
(which I see as sin/sin+cos/sin)
But sin x/sin x = 1, and
cos x/sin x = cot x
so the sum is 1 + cot x.
not quite, but you are close
(sinx + cosx)/sinx
= sinx/sinx + cosx/sinx
= 1 + cotx
you left out the "1"
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