Question

1. sin 30 - cos 45° - sin 60° * tg 30° = ?

2. tg 60° * sin 45° - ctg 45° * cos 60 °= ?

Answer 1

Răspuns:

1.  $- \frac{\sqrt{2} }{2}$

2.  $\frac{\sqrt{6}-1 }{2}$

Explicație pas cu pas:

1.

$sin30 = \frac{1}{2}$

$cos45 = \frac{\sqrt{2} }{2}$

$sin60 = \frac{\sqrt{3} }{2}$

$tg30 = \frac{\sqrt{3} }{3}$  

$sin30 - cos45 - sin60 *tg30 = \frac{1}{2} - \frac{\sqrt{2} }{2} - \frac{\sqrt{3} }{2} *\frac{\sqrt{3} }{3}$

$= \frac{1-\sqrt{2} }{2} - \frac{3}{6}$

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

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

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

2.

$tg 60 = \sqrt{3}$

$sin45 = \frac{\sqrt{2} }{2}$

$ctg 45 = 1$

$cos 60 = \frac{1}{2}$

$tg60 * sin45 - ctg45 *cos60 = \sqrt{3} * \frac{\sqrt{2} }{2} - 1*\frac{1}{2}$

$= \frac{\sqrt{6} }{2} - \frac{1}{2}$

$= \frac{\sqrt{6} - 1}{2}$