(csc x - sin x)(sec x - cos x)(tan x + cot x)
Matematika
redhappyvirus
Pertanyaan
(csc x - sin x)(sec x - cos x)(tan x + cot x)
1 Jawaban
-
1. Jawaban DB45
cssc x = 1/sin x
sec x = 1/cos x
tan x = sin x/ cos x
cot x = cos x/sin x
(csc x - sin x )(sec x - cos x)(tan x + cot x)=
= (1/sin x - sin x) (1/cos - cos x)( sin x /cos x + cos x /sin x)
= {(1 - sin² x) (1 - cos² x)/(sin x cos x )}(sin² x + cos² x)/(sin x cos x)
= (cos² x)(sin² x) (sin²x + cos² x) / (sin x cos x)
= (sin x cos x)² (1) / (sin x cos x)
= sin x cos x