Question

(sec x × cosec x - cot x)(sin x - cosec x )= -cos x

Answer 1

Jadi, apa pertanyaannya?

Edit:

(sec x cosec x - cot x)(sin x - cosec x) = - cos x

(\(frac{1}{cos x}\) \frac{1}{sinx} - \frac{1}{tan x}) (sin x - \frac{1}{sin x}) = - cos x

berhubung tan x = sinx/cosx, maka 1/tanx = cosx/sinx.

(\frac{1}{cosx sinx} - \frac{cosx}{sinx})(\frac{sin^2 x - 1}{sin x}) = - cos x

(\frac{1 - cos^2 x}{cosx sinx})(\frac{sin^2 x -1}{sin x}) = - cos x

Ingat kalau sin^2 x + cos^2 x = 1 (putar2 saja kalau mau tau sin^2 berapa atau cos^2 x), maka:

(\frac{sin^2 x}{cosx sinx})(\frac{-cos^2 x}{sin x}) = - cos x

\frac{-cos^2 x sin^2 x}{cosx sin^2 x} = -cos x

-cos x = - cos x

nah, sama tuh.. tadi nulis format latexnya susah jadi keselimpet ngitungnya hehe 

Answer 2

( .  - ) ( sin x - 
= () ()
= (sin²x - 1 - cos²x sin²x + cos²x) : cos x sin²x
=
= - cosx