Question

Докажите тождество пожалуйста

Answer 1

$frac{cos^22a-4cos^2a+3}{cos^22a+4cos^2a-1} =tg^4a\\ frac{cos^22a-4cos^2a+3sin^2a+3cos^2a}{cos^22a+4cos^2a-sin^2a-cos^2a} = frac{sin^4a}{cos^4a} \\ frac{cos^22a-cos^2a+3sin^2a}{cos^22a+3cos^2a-sin^2a} = frac{sin^2a*sin^2a}{cos^2a*cos^2a} \\ frac{ frac{1+cos4a-1-cos2a+3-3cosa}{2} }{ frac{1+cos4a+3+3cos2a-1+cos2a}{2} } = frac{ frac{(1-cos2a)^2}{4} }{ frac{(1+cos2a)^2}{4} } \\ frac{1+cos4a-1-cos2a+3-cos2a}{1+cos4a+3+3cos2a-1+cos2a} = frac{1-cos2a+cos^22a}{1+2cos2a+cos^22a}$$frac{cos4a-2cos2a+3}{cos4a+4cos2a+3} = frac{1-co2a+ frac{1+cos4a}{2} }{1+2cos2a+ frac{1+cos4a}{2}} \\ frac{cos4a-2cos2a+3}{cos4a+4cos2a+3} = frac{2-2cos2a+1+cos4a}{2+4cos2a+1+cos4a} \\ frac{cos4a-2cos2a+3}{cos4a+4cos2a+3}=frac{cos4a-2cos2a+3}{cos4a+4cos2a+3}\\1=1$

Answer 2

ты докажи тождество =tg^4 a

Answer 3

ну так я и доказал