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Malumtt
@Malumtt
December 2019
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Determine o valor de a sabendo que sec x= a + 1 e tg x= a
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camilisilverio
tg x = a + 1
cotg x = a + 1
tg x = cotg x
sen x/cos x = cos x/sen x
sen²x = cos²x
sen²x -cos²x = 0
De tg x = a + 1, temos que sen x = cos x(a + 1). Então:
(cos x(a + 1))² -cos²x = 0
cos²x(a² +2a +1) -cos²x = 0
cos²x(a² +2a) = 0
a² +2a = 0
Δ = b² -4ac
Δ = 2² -4(1)(0)
Δ = 4
a = (-2±2)/2
a' = -2
a'' = 0
Resposta: a = -2 ou a = 0
Espero ter ajudado
1 votes
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Lista de comentários
cotg x = a + 1
tg x = cotg x
sen x/cos x = cos x/sen x
sen²x = cos²x
sen²x -cos²x = 0
De tg x = a + 1, temos que sen x = cos x(a + 1). Então:
(cos x(a + 1))² -cos²x = 0
cos²x(a² +2a +1) -cos²x = 0
cos²x(a² +2a) = 0
a² +2a = 0
Δ = b² -4ac
Δ = 2² -4(1)(0)
Δ = 4
a = (-2±2)/2
a' = -2
a'' = 0
Resposta: a = -2 ou a = 0
Espero ter ajudado