Question

sec-tan=cos/1+sin
I have to get the left to become the right without changing the right hand side using trig fomulas

Answer 1

So how can you rewrite the left-hand side to start out?

Answer 2

yes

Answer 3

No, how would you do it? Just making sure you know how to start, lol.

Answer 4

I changed the sec and tan to 1/cos and sin/cos

Answer 5

Right. And both of those fractions have a denominator of cos and can thus be combined into
\(\frac{1-sinx}{cosx}\)
I'm sure that makes sense.
From there, the trick is to multiply top and bottom by the conjugate of the numerator. As in multiply top and bottom by 1+sinx. So what would the numerator become if you wee to do that?

Answer 6

(1-sin^2)/cos(1+sin)?

Answer 7

Exactly. And you can use an identity on the \(1-sin^{2}x\)

Answer 8

cos^2/(1+sin)

Answer 9

RIght, you would now have
\[\frac{ \cos^{2}x }{ cosx(1+sinx) }\]
which from there you can seen how one of the cosines would cancel and youd have the result youre looking for :)

Answer 10

thank you so much

Answer 11

No problem :)