Question

help

Answer 1

the identity that includes tan is
1 + tan²x = sec²x

so you are correct :)
the first and last are true

Answer 2

There are only two. What do you mean by first and last and second?

Answer 3

Oh, the third one is a separate question. I thought it applied to the first two. Never mind.

Answer 4

Here is a list of standard trigonometric identities:
http://www.sosmath.com/trig/Trig5/trig5/trig5.html

Answer 5

You will notice the first equation listed under "Double Angle Formulas".
Look for cos(2u) = 1 - 2sin^2(u)
which is the same as your first one and therefore it is an IDENTITY.
Identity implies it is true for ALL values of u (or y in this case).

An equation is true only for some values, not all.

Answer 6

First is an identity and therefore true for ALL values of y.

The second one can be written as: cot^2(x) = 1 + tan^2(x).
But there is a standard trig identity that says: sec^2(x) = 1 + tan^2(x) which is true for all values of x. Therefore, cot^2(x) = 1 + tan^2(x) is NOT an identity. It is an equation which can be solved to find a few values of x for which it is true.
So the second one is false.

The third one is true. Some trig equations are identities. As we saw, the first equation is an identity and the second equation is just an equation and not an identity.

Answer 7

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