Question

TRUE or FALSE! :)

tan^2 x + sec^2 x = 1 for all values of x.

***My answer: False

is that right? @terenzreignz :)

Answer 1

that's right :)
-tan^2 x + sec^2 x = 1
is true for all values.

:)

Answer 2

ohhh i see :) so this is TRUE right?

Answer 3

No, I said you were correct :P

Answer 4

I said it would be true for all possible values of x if it were
-tan^2 x instead

Answer 5

TRUE or FALSE! :)

cos2a=1-2sin^2 a for all values of a.

***MY answer: FALSE

is that right? :)

and ohhh okay haha i see :) yay! thanks! :D

Answer 6

what do u think of that one @terenzreignz :)

Answer 7

Well, problem.
You know the pythagorean identity
\[\large \cos^2x + \sin^2 x = 1\]
from which you can derive
\[\large \color{red}{\cos^2x }= \color{blue}{1-\sin^2x}\]

And the eerily similar formula for the double angle identity of cosine
\[\large \cos(2x) = \color{red}{\cos^2x }- \sin^2x\]
Here you can replace the \(\large \cos^2x\) as prescribed by our identity...
\[\large \cos(2x) = \color{blue}{1-\sin^2x}-\sin^2x\]\[\large \cos(2x) = 1-2\sin^2x\]

Answer 8

ohhh okay... so it's true then right ?

cuz we end up with this?

cos2a=1-2sin^2a

just a instead of the x tho? so TRUE?!

Answer 9

Yes, true.

Answer 10

okay! thanks! :D