cost+tantsint=sect

Question

i need to prove this with trigonometric identities, i'm kind of lost. thanks.

Answer 1

cost+tant sint=sect; we can replace tan t for sint/cost

cost + (sint*sint)/ cos t = sect

making common denominator we have:

(cos²t + sin²t)cos t = sec t

The numerator is equal to 1 so:

1/cos t  = sec t; and 1/cos t equals sec t so the equality was shown!!!!!!!!!!!!!!!!!!!!!!!