Question

24*(sin 15 - cos 15)/cos 30 =

Answer 1

Ответ:

$-8\sqrt{6}$

Объяснение:

24*(sin 15 - cos 15)/cos 30  =  24*( sin(60°-45°) - cos(60°-45°) ) /cos 30°  =

Используем формулу: sin (x-y) = sin x * cos y - cos x * sin y

                                        cos (x-y) = cos x * cos y + sin x * sin y

=  24* ( (sin 60 *cos 45 - cos 60 * sin 45) - (cos 60 * cos 45 + sin 60 * sin 45) ) /cos 30   =   24* (sin 60 *cos 45 - cos 60 * sin 45 - cos 60 * cos 45 - sin 60 * sin 45 ) /cos 30   =   24*( $\frac{\sqrt{3} }{2} * \frac{\sqrt{2} }{2} - \frac{1}{2} * \frac{\sqrt{2} }{2} - \frac{1}{2} * \frac{\sqrt{2} }{2} - \frac{\sqrt{3} }{2} * \frac{\sqrt{2} }{2}$ ) / $\frac{\sqrt{3} }{2}$   =   24*( -$\frac{\sqrt{2} }{2}$) / $\frac{\sqrt{3} }{2}$ = $\frac{24*(-\sqrt{2}) }{2} / \frac{\sqrt{3} }{2}$   =   $\frac{24*(-\sqrt{2}) *2 }{2 * \sqrt{3} }$   =   $\frac{24*(-\sqrt{2}) }{ \sqrt{3} }$   =   $-\frac{24*(\sqrt{6}) }{ 3 }$   =   $-8\sqrt{6}$

Answer 2

To evaluate the expression 24*(sin 15 - cos 15)/cos 30, we can start by calculating the values of sin 15, cos 15, and cos 30.

sin 15 ≈ 0.2588 cos 15 ≈ 0.9659 cos 30 ≈ 0.8660

Now we can substitute these values into the expression:

24*(sin 15 - cos 15)/cos 30 = 24*(0.2588 - 0.9659)/0.8660

Simplifying further:

= 24*(-0.7071)/0.8660 = -16.5651/0.8660 ≈ -19.111

Therefore, 24*(sin 15 - cos 15)/cos 30 is approximately equal to -19.111.