Question

sen^2 x + 5 cos^2 x = 3 com 0 < x < pi/2 calcule sen x e cos x

Answer 1

Resposta:

Explicação passo-a-passo:

sen²x + 5cos²x = 3

Mas sen²x + cos²x = 1

sen²x = 1 - cos²x

Subst. vem

1 - cos²x + 5cos²x = 3

4cos²x = 3 - 1

4cos²x = 2

cos²x = 2/4

cos²x = 1/2

$cosx =\sqrt{\frac{1}{2}}\\\\cosx=\frac{1}{\sqrt{2}}\\\\cosx=\frac{\sqrt{2}}{2}$

sen²x = 1 - cos²x

sen²x = 1 - 1/2

senx² = 1/2

$senx=\frac{\sqrt{2} }{2}$

Resp. $senx = cosx=\frac{\sqrt{2}}{2}$