Question

Simplify the expression: \[(\tan \Theta+1)(\tan \Theta-1)\]

Answer 1

See how each set of brackets contains the same thing except with a sign change?
These are CONJUGATES.

When you multiply conjugates you get the difference of squares.
Example:\[\large (x-y)(x+y)=x^2-y^2\]

Answer 2

cot^2 thaeta?

Answer 3

what about \[\tan^{2} \Theta-1\]

Answer 4

Yup looks good! c:

And since we don't have an identity for tan^2 - 1, it looks like that's as far as we can simplify it.

Answer 5

got it. thanks!