Question

Упростить выражение:

Answer 1

tg^2(b)=sin^2(b)/cos^2(b)
ctg^2(b)=cos^2(b)/sin^2(b)
1). (sin^2(b)-sin^2(b)*cos^2(b))/cos^2(b)=sin^2(b)*(1-cos^2(b)/cos^2(b)
2). Аналогично: cos^2(b)*(1-sin^2(b)/sin^2(b)
3). (sin^2(b)*(1-cos^2(b)))/cos^2(b))*(sin^2(b)/(cos^2(b)*(1-sin^2(b)))= sin^4(b)*(1-cos^2(b))/(cos^4(b)*(1-sin^2(b)))= tg^4(b)*sin^2(b)/cos^2(b)=tg^6(b). 1-sin^2(b)=cos^2(b)
1-cos^2(b)=sin^2(b)
по основному правилу: sin^2(x)+cos^2(x)=1