Question

упростить 1-sin2x/sinx-cosx

Answer 1

Ответ 1:

1 - 3cos(x)

Объяснение 1:

$1-\frac{sin(2x)}{sin(x)} -cos(x)= 1-\frac{2sin(x)cos(x)}{sin(x)}-cos(x)= 1-2cos(x)-cos(x)=1-3cos(x)$

Ответ 2:

sin(x) - cos(x)

Объяснение 2:

$\frac{1-sin(2x)}{sin(x)-cos(x)} = \frac{1-2sin(x)cos(x)}{sin(x)-cos(x)} = \frac{sin^2(x)+cos^2(x)-2sin(x)cos(x)}{sin(x)-cos(x)} = \frac{(sin(x)-cos(x))^2}{sin(x)-cos(x)} = sin(x)-cos(x)$