Question

Prove: sec x(1 + cos x) = 1 + sec x

Answer 1

see secx*cosx=1

Answer 2

distribute!

Answer 3

\[\sec(x) = \dfrac{1}{\cos(x)}\]So\[\dfrac{1}{\cos(x)}\left(1 + \cos(x)\right) = 1 + \dfrac{1}{\cos(x)}\]Distribute\[\dfrac{1}{\cos(x)} + 1 = 1 + \dfrac{1}{\cos(x)}\]Don't need to go further

Answer 4

The left hand side is just the right hand side, right?

Answer 5

Presumably

Answer 6

So we're done.

Answer 7

Could be shorter by memorizing \(\sec(x) \times \cos(x) = 1\), but bleh :p

Answer 8

wouldn't you prove it like:

secx+secx*cosx
=secx+1/cosx*cosx
=secx+1

Answer 9

Yeah, that's the shorter way to prove it.

Answer 10

:D

Answer 11

can you elaborate @isuckatmath9999 ? :)i mean elaborate your way. haha

Answer 12

lol there are about 5000* ways, anyone else got another?

Answer 13

@Jhannybean \(\sec(x) \times \cos(x) = 1\)

Answer 14

I don't neeed another its for an assignment lol. :)

Answer 15

yeahhh but how'd he get...sec (x) + 1/cos^2 (x)...

Answer 16

OH YOU FACTORED OUT THE SEC (X)???

Answer 17

yea lol

Answer 18

It's not 1/cos^2(x) lol
It's 1/cos(x) * cos(x)

Answer 19

oh ho ho, i gotchu.

Answer 20

I have more questions to debate upon lol. don't worry :P heheee

Answer 21

I haven't done trig in months. Wow

Answer 22

there isn't one

Answer 23

i feel so dyslexic...