Question

1. buktikan (cos x + sin x ) ( cos x - sin x ) = 1 - 2 sin² x
2. buktikan sin x cos x ( tan x + cot x ) = 1
3. buktikan cot x + tan x / sec x = csc x

Answer 1

Verified answer

Identitas

ruas kiri =  ruas kanan

1. (cos x + sin x)(cos x- sin x) = 1 - 2 sin² x
(cos x + sin x)(cos x - sin x) =
= cos² x - sin² x
= (1 - sin² x)  - sin² x
= 1 - sin² x - sin² x
= 1 - 2 sin² x

2. sinx cos x (tan x + cot x) = 1
sin x cos x (sin x /cos x + cos x/sin x)
sin x cos x ( sin² + cos² x)/(cos x sin x)
= sin² x + cos² x
= 1

3. (cot x + tan x)/ (sec x ) = csc x
ruas kiri
(cot x + tan x) /(sec x) =
= {(cos x/sin x + sin x/cosx )} /(1/cos x)
= {(cos² x + sin² x) / (sin x cos x)}  . (cos x)
=  {1 / (sin x cos x )} . (cos x)
= cos x / sin x  cos x
= 1/sin x
= csc x