Question

Calculati
a )sin 45 cos 30 -sin 30 cos 45
b )sin² 30 +cos² 30
c )tg 60 · ctg 60
d ) tg 30 +ctg 30

Answer 1

a)
$\dfrac{\sqrt2}{2}\cdot\dfrac{\sqrt3}{2}-\dfrac12\cdot\dfrac{\sqrt2}{2}=\dfrac{\sqrt2}{4}(\sqrt3-1)$
b)
...=1, deoarece $sin^2x+cos^2x=1,\ pentru \ orice \ x.$
c)
tgx·ctgx=1, pentru orice x, deci si pentru 60 grade.

d) $...=\dfrac{\sqrt3}{3}+\sqrt3=\dfrac{4\sqrt3}{3}$