Question

Sendo cosx = 1/m e senx = √m+1/m, determine m.

Answer 1

cos x = 1/m e sen x = √(m+1) /m

sen²x + cos²x = 1

(√(m+1) /m)² + (1/m)² = 1

(m+1)/m² + 1/m² = 1

[m + 1 + 1]/m² = 1

(m+2)/m² = 1

m² . 1 = m + 2

m² = m + 2

m² - m - 2 = 0

∆ = b² - 4ac

∆ = (-1)² - 4(1)(-2)

∆ = 1 + 8

∆ = 9

m' = -(-1) + √9 / 2.1

m' = 1 + 3/2

m' = 4/2

m' = 2

m'' = -(-1) - √9 /2.1

m'' = 1 - 3 /2

m'' = -2/2

m'' = -1

S = {-1, 2}

Letra D.

Answer 2

Sen²x + cos²x = 1

$\frac{1}{m²}$ + $\frac{m+1}{m}$ =1

1/m² + (m²+m)/m² = 1

1 + m² +m = m²

m= -1