Question

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Answer 1

1)a) $sin(alpha+beta)-2sinbeta*cosalpha=sinalpha*cosbeta+cosalpha*sinbeta-2sinbeta*cosalpha$=$sinalpha*cosbeta-sinbeta*cosalpha=sin(alpha-beta)=1$
b)  $sin^2alpha-frac{cos(frac{pi}{2}+alpha)*sin(pi-alpha)}{tg(pi-alpha)*ctg(frac{3*pi}{2}+alpha)}}=sin^2alpha-frac{-sinalpha*sinalpha}{-tgalpha*-tgalpha}=sin^2alpha-cos^2alpha$
2) $(cos32circ+cos28circ)^2+(sin32circ-sin28circ)^2=0.25+0.005=0.255$
3) $cos=sqrt{1-sin^2}=sqrt{frac{169}{169}-frac{144}{169}}=frac{5}{13}$ ; $sin2alpha=2*sin*cos=2*frac{-12}{13}*frac{5}{13}=frac{-120}{169}$ ; $cos2alpha=cos^2-sin^2=frac{25}{169}-frac{144}{169}=-frac{119}{169}$