Question

Buktikan identitas trigonometri
1. cos x/ 1- tan x + sin x/ 1- cotan x = sin x + cos x

Answer 1

[cos x / (1 - tan x)] + [ sin x /(1 - cotan x)] = sin x + cos x
[ cos x /{1 - (sin x/cos x)}] + [ sin x /{1 - (cos x /sin x)}] =
[ cos x /{ (cos x - sin x) /cos x}] + [ sin x / {(sin x - cosx) / sin x}] =
[cos x . {cos x / (cos x - sin x)}] + [ sin x . {(sin x /(sin x - cos x)}] =
[ cos² x / (cos x - sin x)] + [ sin² x / ( sin x - cos x)] = 
[cos² x / (cos x - sin x) ] + [ sin² x / - (cos x - sin x)] = 
[ cos² x / (cos x - sin x)] - [ sin² x /(cos x - sin x)] =
(cos² x - sin² x) / (cos x - sin x) =
[(cos x + sin x) (cos x - sin x)] / (cos x - sin x) =
 cos x + sin x =
 sin x + cos x   ....... terbukti ....