Question

Calculati:
a) sin 30°. tg 45° + cos 30°. ctg 60°
b) sin 60° . cos 60° + sin 30°. cos 30°
- sin 45º. cos 45º​

Answer 1

Răspuns:

a) sin 30° * tg 45° + cos 30° * ctg 60° = $\frac{1}{2}$* 1 + $\frac{\sqrt{3} }{2}$ *$\frac{\sqrt{3} }{3}$ = $\frac{1}{2}$*$\frac{3}{6}$=$\frac{1}{4}$

b) sin 60° * cos 60° + sin 30° * cos 30° - sin 45° * cos 45° = $\frac{\sqrt{3} }{2}$*$\frac{1}{2}$ + $\frac{1}{2}$*$\frac{\sqrt{3} }{2}$ - $\frac{\sqrt{2} }{2}$ * $\frac{\sqrt{2} }{2}$

=$\frac{\sqrt{3} }{4}$ + $\frac{\sqrt{3} }{4}$ - $\frac{1}{2}$ = $\frac{2\sqrt{3} }{4}$  - $\frac{2}{4}$  = $\frac{2(\sqrt{3}-2) }{4}$ = $\frac{\sqrt{3}-2 }{2}$