Question

430(1,3) ииии 432(1)

Answer 1

$1); tg( frac{3pi}{2}+a)tg(pi -a)+cos(frac{pi}{2}+a)sin(pi -a)=\\=-ctga cdot (-tga)-sinacdot sina=1-sin^2a=cos^2a\\2); ; Big (ctg(6,5pi -a)cdot cos(-a)+cos(pi -a)Big )^2+2sin^2(pi -a)cdot ctg(a-pi )\\=Big (-ctgacdot cosa-cosaBig )^2+2sin^2acdot (-ctga(-a))=\\=cos^2acdot (ctga+1)^2+2sin^2acdot frac{cosa}{sina}=\\=cos^2acdot (frac{cosa}{sina}+1)^2+2sinacdot cosa=cos^2acdot frac{(cosa+sina)^2}{sin^2a}+sin2a=\\=ctg^2a(1+sin2a)+sin2a=ctg^2a+sin2a(ctg^2a+1)=$

$=ctg^2a+sin2acdot frac{1}{sin^2a}=ctg^2a+frac{2sinacdot cosa}{sin^2a}=ctg^2a+2ctga=ctga(ctga+2)$

$3); ; (ctga-cosa)(sina+tga)= \\=frac{cosa}{sina}cdot sina +ctgacdot tga-cosacdot sina -cosacdot frac{sina}{cosa} =\\=cosa+1-cosacdot sina-sina=(cosa+1)-sinacdot (cosa+1)=\\=(1+cosa)cdot (1-sina)$