Question

Bentuk sederhana 1 + sec x / tan x + sin x=...

tolong dijawab ya pake cara.

Answer 1

1 + sec x / tan x + sin x

=
(1 + 1/cosx) /( sinx/cosx + sinx)
=
[cosx+1 / cosx ] / [ sinx+sinxcosx / cosx]
=
cosx+1 / cosx kali cosx/ sinx+sinxcosx

=
cosx+1 / sinx+sinxcosx kali cosx-1 / cosx-1

= cos²x-1 / sinx(1+cosx) (cosx-1)
= cos²x-1/ sinx(-1+cos²x)
= cos²x - 1 / sinx.(cos²x-1)
= 1 / sinx
atau
cosecx