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mursalovasuriya

 x : prinadlejit : 4oy : cetverti \ sin(x)  =  -  frac{5}{13}  \  {cos}^{2} x +  {sin}^{2} x = 1 \  {cos}x =  sqrt{1 - {sin }^{2} x}   =   \  = sqrt{1 - ( { frac{5}{13} }^{2}) }  =  sqrt{1 -  frac{25}{169} }  =   \  = sqrt{ frac{144}{169} }  =  frac{12}{13}

1)cos2x =  { (frac{12}{13}) }^{2}  -  { ( - frac{5}{13}) }^{2}  =  \  =  frac{144}{169}  -  frac{25}{169}  =  frac{119}{169}

tgx =  frac{sinx}{cosx}  =  frac{  - frac{5}{13} }{ frac{12}{13} }  =  \  =  -  frac{5}{12}

2)tg2x =  frac{2tgx}{1 -  {tg}^{2} x}  =  \  =  frac{2( -  frac{5}{12} )}{1 -  {( -  frac{5}{12}) }^{2} }  =  -  frac{ frac{5}{6} }{ frac{119}{144} }  =    \  = - frac{5 times 144}{6 times 119}  =   - frac{120}{119}

ctgx =  frac{cosx}{sinx}  =  \  =  frac{ frac{12}{13} }{ -  frac{5}{13} }  =  -  frac{12}{5}

3)ctg2x =  frac{  {ctg}^{2} x - 1}{2ctgx}  =  \  =  frac{ frac{144}{25}  - 1}{2 times ( - frac{12}{5})  }  =  \  =   - frac{ frac{119}{25} }{ frac{24}{5} }  =  -  frac{119 times 5}{25 times 24}  =  -  frac{119}{120}

4)sin2x=2sinxcosx=2×(-5/13)×(12/13)=

=-120/169

5)cos(п/6+х)=cos(п/6) cosх-sin(п/6) sinх=

=(корень3)/2 * (12/13)-(1/2)*(-5/13)=

=[12(корень3)+5]/26

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