Question

Secx . (secx - cosx)= tg^2x

Answer 1

Sec(x)*[sec(x) - cos(x)] = tan²(x)

cos(x) = 1/sec(x)

sec(x)*[sec(x) - (1/sec(x))]

Rompo el parentesis

sec²(x) - sec(x)*[1/sec(x)] = sec²(x) - 1

Recordemos

1 + tan²(x) = sec²(x)

despejando tan²(x)

tan²(x) = sec²(x) - 1

 
sec(x)*[sec(x) - cos(x)] = sec²(x) - 1

sec(x)*[sec(x) - cos(x)] = tan²(x)