" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
poniewaz (sinα) ²+(cosα) ²=1
Oblicz W = (sinα - cosα)² = sin²α -2sinα*cosα + cos²α = 1 -2sinαcosα=
= 1 -2*(1/2) = 1 - 1 = 0
z wzorów skróconego mnożenia :
(a-b)²=a²-2ab+b²
a=sinα
b=cosα
mamy:
(sinα - cosα) ²=sin²α-2sinα *cosα+cos²α=sin²α+cos²α-2sinα *cosα
wiadomo również, że:
sin²α+cos²α=1
z treści:
sinα * cosα = ½
zatem:
(sinα - cosα) ²=(sin²α+cos²α)-2(sinα *cosα)=1-2*½=1-1=0