Question

tgx . (ctgx + tgx)= sec^2x ayuda PLS

Answer 1

Tan(x)*[ctan(x) + tan(x)] = sec²(x)

Ctan(x) = 1/tan(x)

tan(x)*[(1/tan(x)) + Tan(x)]

Tan(x)*[1/Tan(x)] = 1

Tan(x)*[Tan(x)] = Tan²(x)

Tan(x)*[ctan(x) + tan(x)]  = 1 + Tan²(x)

Por identidades trigonometricas sabemos

1 + tan²(X) = Sec²(X)

Tan(x)*[ctan(x) + tan(x)]  = Sec²(x)

Si se cumple la identidad