Question

sprawdź tożsamość:

2cos(kwadrat)x - 1 = [1- tg(kwadrat)x]/[1+ tg(kwadrat)x]

Answer 1

 

 

P = (1 - tg^2 x)/( 1 + tg^2 x) = ( 1- ( sin ^x)/(cos^x))/(1 + (sin^2)/(cos^2x)) =

= [ cos^x/ cos^2x - sin^x/cos^2 x]/[ cos^2x /cos^2x + sin^2x/ cos^2 x] =

= [( cos^2x - sin^x)/ cos^2x]/[(cos^2x + sin^2x)/cos^2 x] =

= [(cos^2x - sin^2x)/ cos^x] *[ cos^2 x / 1] = cos^2 x - sin^2 x =

= cos^2 x - ( 1 - cos^2 x)  = 2 cos^2 x - 1 = L