Question

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Answer 1

1)a) $sin(\alpha+\beta)-2sin\beta*cos\alpha=sin\alpha*cos\beta+cos\alpha*sin\beta-2sin\beta*cos\alpha$=$sin\alpha*cos\beta-sin\beta*cos\alpha=sin(\alpha-\beta)=1$
b)  $sin^2\alpha-\frac{cos(\frac{\pi}{2}+\alpha)*sin(\pi-\alpha)}{tg(\pi-\alpha)*ctg(\frac{3*\pi}{2}+\alpha)}}=sin^2\alpha-\frac{-sin\alpha*sin\alpha}{-tg\alpha*-tg\alpha}=sin^2\alpha-cos^2\alpha$
2) $(cos32\circ+cos28\circ)^2+(sin32\circ-sin28\circ)^2=0.25+0.005=0.255$
3) $cos=\sqrt{1-sin^2}=\sqrt{\frac{169}{169}-\frac{144}{169}}=\frac{5}{13}$ ; $sin2\alpha=2*sin*cos=2*\frac{-12}{13}*\frac{5}{13}=\frac{-120}{169}$ ; $cos2\alpha=cos^2-sin^2=\frac{25}{169}-\frac{144}{169}=-\frac{119}{169}$