Question

Help with trigonometric identities?

Answer 1

Write \[\tan ^{2}x-\sec ^{2}x\] in terms of sin and cos, then simplify.

Answer 2

what have you got so far?

Answer 3

\[\frac{ \sin ^{2}x }{ \cos ^{2}x } - \frac{ 1}{\cos ^{2}x }\]

Answer 4

any ideas what to do next?

Answer 5

Well my initial thought was to simply subtract 1 from sin^2x but that's not correct

Answer 6

oh its correct, but what you really ned to focus on is your pythagorean identity

Answer 7

s^2+c^2 =1

can we work this into s^2-1 ?

Answer 8

Wait, if sin^2+cos^2=1, then sin^2-1 is just cos^2, right? So it's -cos^2/cos^2 or -1?

Answer 9

better yet

s^2 +c^2 - 1, divide by c^2

s^2/c^2 +c^2/c^2 =1/c^2

tan^2 + 1 = sec^2

tan^2 - sec^2 =-1

yes

Answer 10

typo in first line ... =1

Answer 11

but yeah,-1 is the simplification