## anonymous one year ago Could someone please help me verify the trig. equation using identities? 1+sec^2xsin^2x=sec^2x

1. anonymous

you could start by the first part of the equality $1+\sec^{2}x*sen^{2}x$ you have to remember these identities : $secx=1/cosx$ $sen^{2}x+cos^{2}x=1$ replacing $1+\frac{ 1^{2} }{\cos^{2}x }*sen^{2}x$ $\frac{ cos^{2}x+sen^{2}x }{\cos^{2}x}$ $\frac{ 1 }{\cos^{2}x}=sec^{2}x$

2. anonymous

Thanks so much! @baad1994 Could you help me with one more? -5tan^2x+sec^2x=1

3. anonymous

And haha, I actually understood what steps you took. (: So thank you so much!!

4. anonymous

nice! :) , are you sure that there is a 5 before tan^2x?

5. anonymous

Oh, sorry. I meant -tan^2x not 5tan^2x

6. anonymous

oh ok , no problem n.n $-tg^{2}x+\sec^{2}x=1$ the same, start by the first part $-tg^{2}x+\sec^{2}x$ Remember these: 1)$tgx=\frac{ senx }{ cosx }$ 2)$secx=\frac{ 1 }{ cosx }$ 3)$sen ^{2}x+\cos ^{2}x = 1$ $\cos ^{2}x = 1-sen ^{2}x$ replacing $-\frac{ senx^{2} }{ cosx^{2} }+\frac{ 1 }{ cosx^{2} }$ $\frac{ 1-sen^{2}x }{ \cos ^{2}x }$

7. anonymous

when you are going to verify trigonometric expressions you usually have to pass all to sen and cos. And remember that sen^2x+cos^2x=1

8. anonymous

so remember the equivalences: secx=1/cosx cscx=1/senx tgx=senx/cosx ctgx=cosx/senx and operate

9. anonymous

Thanks so much!! (: