Question

Verifique as identidades
A) secx . Cotg^2x . Senx=cotgx
B) 1-sen^2x/cotgx . Senx=cosx
C) (secx-tgx)(secx+tgx)=1

Answer 1

A)

secx . Cotg^2x . Senx=cotgx

=1/cos(x) * (cos²(x)/sen²(x)) * sen(x)

=cos(x)/sen(x) =   cotg (x)    ..OK

 B)

(1-sen²x)/[cotg(x) . sen(x)] =cos(x)

(1-sen²x)/[cotg(x) . sen(x)] =cos(x)

cos²x/[(cos(x)/sen(x)) . sen(x)] =cos(x)

cos²x/[(cos(x)]=cos(x)   ..ok

 C)

 (secx-tgx)(secx+tgx)=1

sec²(x) -tg²(x)=1

1/cos²(x)  -sen²(x)/cos²(x)

=(1-sen²(x)/cos²(x)

=cos²(x)/cos²(x) = 1 ..OK