Question

Me ajudem:
senX + cosX + tgX + secX + cossecX + cotgX= ?
Dados: SenX= 1/4

Answer 1

Olá,

Precisamos calcular todos eles:
senx = 1/4

sen²x + cos²x = 1
(1/4)² + cos²x = 1
cos²x = 1 - 1/16
cos²x = 15/16
cosx = √15/4

tgx = senx/cosx
tgx = (1/4)/(√15/4)
tgx = (1/4)*(4/√15)
tgx = 4/4√15
tgx = 1/√15
tgx = √15/15

secx = 1/cosx
secx = 1/(√15/4)
secx = 1*4/√15
secx = 4/√15
secx = 4√15/15

cossecx = 1/senx
cossecx = 1/(1/4)
cossecx = 1*4/1
cossecx = 4

cotgx = cosx/senx
cotgx = (√15/4)/(1/4)
cotgx = (√15/4)*(4/1)
cotgx = 4√15/4
cotgx = √15

Somando tudo, temos:
1/4 + √15/4 + √15/15 + 4√15/15 + 4 + √15
(1 + √15)/4 + (√15 + 4√15)/15 + 4 + √15
(1 + √15)/4 + (5√15)/15 + 4 + √15
(1 + √15)/4 + √15/3 + 4 + √15
(3 + 3√15 + 4√15)/12 + 4 + √15
(3 + 7√15)/12 + 4 + √15
(3 + 7√15 + 48 + 12√15)/12
(19√5 + 51)/12

Bons estudos ;)

Answer 2

Resposta:

17+20√15/4

Explicação passo-a-passo: