Question

Sa se calculeze sin170 la 0 -sin10 la 0
sin la 2 80 la 0 + sin la 2 10 la 0
tg la 2 30 la 0 + ctg la 2 45 la 0
cos 10 la 0+ cos 20 la 0 +cos160 la 0 +cos 170 la 0
Calculati valoarea expresiei sin la 2 10 grade +sin la 2 80 grade
clasa 9 ajutati.ma va roggg

Answer 1

   
[tex]1) \\ sin\,170^o -sin\,10^o = \\ = sin\,(180^o-10^o) -sin\,10^o = \\ = sin\,10^o -sin\,10^o =\boxed{0} \\ \\ 2) \\ sin^2 80^o + sin^2 10^o= \\ = sin^2 80^o + sin^2 (90^o-10^o)= \\ =sin^2 80^o +cos^2 80^o = \boxed{1} [/tex]

[tex]3) \\ tg^2 30^o + ctg^2 45^o = \\ = \left( \frac{ \sqrt{3} }{3} \right)^2 + 1^2= \\ \\ = \frac{3}{9} +1=\frac{1}{3} +1 = \frac{1}{3}+\frac{3}{3} = \frac{1+3}{3} = \boxed{\frac{4}{3}} \\ \\ 4) \\ cos \,10^o+ cos\,20^o+cos\,160^o +cos\,170^o= \\ =cos \,10^o+ cos\,20^o+cos\,(180^o-20^o) +cos\,(180^o-10^o)= \\ =cos \,10^o+ cos\,20^o-cos\,(20^o) -cos\,(10^o)= \\ =cos \,10^o-cos\,(10^o)+ cos\,20^o-cos\,(20^o) = 0+0 = \boxed{0} [/tex]

[tex]5) \\ sin^2 10^o +sin^2 80^o = \\ =sin^2 10^o + sin^2 (90^o-10^2)= \\ =sin^2 10^o + cos^2 10^o = \boxed{1}[/tex]