Question

Se f(x)= sen x + tan x / cot x + csc x e g(x) = sen x • tan x, provem que f(x) = g(x)

Answer 1

Sabendo que: ctx=1/tgx e secx=1/senx

f(x) = (senx + tgx)/(cotx+cscx)
f(x) = (senx + tgx)/[ (1/tgx) + (1/senx)]
f(x) = (senx + tgx)/[ (senx + tgx)/(tgx.senx)]
f(x) = tgx.senx

∴ f(x)=g(x) c.q.d