Question

which is not an identity?

Answer 1

\[\tan^2x = \sec^2x - \sin^2x - \cos^2x\]

Answer 2

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

Answer 3

\[(cosx + sinx)^2 = 1 + 2cosx sinx\]

Answer 4

\[(tanx + cotx)^2 = \csc^2 x + \sec^2 x\]

Answer 5

numbers 2 and 3 are identities

Answer 6

the first one may be

does it equal sec^2 x = 1 + tan^2 x

Answer 7

oops sin^2 x = 1 - cos^2 x

so what can you say about number 2?

Answer 8

i was wrong - can you see why?

Answer 9

I was wrong about number 2

Answer 10

so it is not an identity?

Answer 11

right because sin^2 x = 1 - cos^2 x NOT 1 + cos^2 x

so 1 + cos^2 x
---------- cannot be equal to 1 for all values of x
sin^2 x

Answer 12

an identity is true for all values of the variable - that is its definition