Question

tan^2(x)-sec^2(-x) simplify the expression

Answer 1

HINT: start with sin^2 x+cos^2 x=1

Answer 2

divide both sides by cos^2 x

Answer 3

x=1?

Answer 4

No, we don't know x

Answer 5

im talking about your hint

Answer 6

no sec²(x)=1+tg²(x)

Answer 7

oh thats an identity

Answer 8

rewrite the tangent and secant as sines and cosines

Answer 9

sec(-x)=sec(x)

Answer 10

so i get sin^2x/cos^2x - 1/cos^2x?

Answer 11

\(\Huge \frac{\sin^2x}{\cos^2 x}-\frac{1}{\cos^2x}\)

Answer 12

yes

Answer 13

sweet so i was on the right track

Answer 14

wait factor it out of what?

Answer 15

\(\frac{1}{\cos^2 x}(\sin^2 x-1)\)

Answer 16

oh so mult both sides by 1/cos^2

Answer 17

Well sort of. It's not an equality, so we can't legally do that. We can only factor out the 1/cos^2

Answer 18

okay thats where i kind of get a bit lost im taking cos out of sin^2x/cos^2x?

Answer 19

Well I just rewrote the expression. distribute it again, and you can see that it is the same