Question

Dados :
$sen :x \: = \: \frac{1}{2}, \: calcular \: o \: valor \: da \: expressao: \: \frac{sen^{2} x - \: 1 }{tg^{2} x + 1}$
Resolução por favor!!!

Answer 1

Olá !

sendo :

senx=1/2


senx²+cosx²=1


(1/2)²+cosx²=1


1/4+cosx²=1


cosx²=1- 1/4


cosx²=4-1/4


cosx²=3/4


cosx=√3/4


cosx=(√3)/2


tgx=senx/cosx


tgx=1/2 /√3/2


tgx=2/2√3


tgx=1/√3


tgx=√3/3


vamos elevar ao quadrado senx e tgx:

tgx²=(√3/3)²=3/9=1/3


senx²=(1/2)²=1/4


senx²-1/ tgx²+1=>


=>1/4-1/1/3+1


=>1-4/4 ÷ 1+3/3


=>-3/4÷4/3


=>4.(-3)/3.4


=>-12/12


=>-1

$resposta= - 1$

espero ter ajudado!

bom dia !

Answer 2

(Sen^2x-1)/(tg^2x+1)

Sec^2x=1+tg^2x

secx=1/cosx

Cos^2x=1-sen^2x

(sen^2x-1)/sec^2x

(Sen^2x-1)/(1/cos^2x)

(Sen^2x-1)(cos^2x)

(sen^2x-1)(1-sen^2x)

-(1-sen^2x)(1-sen^2x)

-(1-2sen^2x+sen^4x)

-(1-2 (1/2)^2+(1/2)^4)

-(1-1/2+1/16)

-(16-8+1)/16

-9/16