Question

r=
$\frac{ \sin(36) }{ \sin(12) } - \frac{ \cos(36) }{ \cos(12) }$
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Answer 1

Răspuns:

2

Explicație pas cu pas:

Aducem fractiile la acelasi numitor apoi folosim formulele de mai jos:

sin(a-b)=sin(a)cos(b)-sin(b)cos(a)

sin(2a)=sin(a+a)=sin(a)cos(a)+sin(a)cos(a)=2sin(a)cos(a)

$\frac{sin(36)}{sin(12)} -\frac{cos(36)}{cos(12)} =\\ =\frac{sin(36)cos(12)}{sin(12)cos(12)} -\frac{cos(36)sin(12)}{sin(12)cos(12)} =\frac{sin(36)cos(12)-sin(12)cos(36)}{sin(12)cos(12)} \\ =\frac{sin(36-12)}{sin(12)cos(12)} =\frac{2sin(24)}{2sin(12)cos(12)} =\frac{2sin(24)}{sin(12+12)} =\frac{2sin(24)}{sin(24)} =2$