Question

Are all true trig equations identities?

Answer 1

Identity is literally defined to be true for all real values of x

Answer 2

If I'm asked to decide whether an equation is a trig identity, would I prove it to be true? That's it?

For example, cos^2x(1 + tan^2x) = 1
It's true... but is it an identity?

Answer 3

So if the equation is true, it's an identity? always?

Answer 4

Here's another one I had:
secxtanx(1-sin^2x) = sinx

I found it to be true, but is it true for all real numbers?

Answer 5

An identity is true, when both sides of the equation are equal to each other. An equation is when inputting a certain value in the variable makes the equality true

Answer 6

That word is really ambiguous...
Identity just refers to how useful the equation is,
so we call it an identity because we use it very often.

I reaaaally hope they're only asking you to determine the truthfulness of the equation, otherwise that really bothers me :\

Answer 7

I think so zep :P I dunno...
D:

Answer 8

The specific instructions say, "decide whether each equation is a trigonometric identity. Explain your reasoning"

Answer 9

Calc = muy bueno, by the way :D (so far)

Answer 10

Oo nice :)
Almost out of the maze of trig?

Answer 11

Almost! If only this question wasn't so ambiguous :|

Answer 12

The best way to find if a trigonometry equation is an identity, is by trying to make both sides look the same, without inputting any values. By algebraic and trigonometric manipulation, try making both sides equal to each other. If done, its an identity, if not, its an equation

Answer 13

Right, okay that's what I've been doing. Thanks Fai !
Do my answers look correct?

Answer 14

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Abbles
If I'm asked to decide whether an equation is a trig identity, would I prove it to be true? That's it?

For example, cos^2x(1 + tan^2x) = 1
It's true... but is it an identity?
\(\color{#0cbb34}{\text{End of Quote}}\)
Yep an identity

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Abbles
Here's another one I had:
secxtanx(1-sin^2x) = sinx

I found it to be true, but is it true for all real numbers?
\(\color{#0cbb34}{\text{End of Quote}}\)
Yep an identity

Answer 15

\[cscx(2sinx-\sqrt{2}) = 0\]
How would I prove/disprove that one? So far I've replaced the cscx with 1/sinx but that's about as far as I got...

Answer 16

It's an equation, not an identity

Answer 17

\(\displaystyle \csc x \left(2\sin x-\sqrt{2}\right)=0\)
\(\displaystyle \csc x \left(2\sin x-\sqrt{2}\right)\color{red}{\cdot \cos x}=0\color{red}{\cdot \cos x}\)
\(\displaystyle2\sin x-\sqrt{2}=0\)
\(\displaystyle2\sin x=\sqrt{2}\)
\(\displaystyle\sin x=\sqrt{2}/2\)

You see that this is an "equation" and it is not an "Identity".
Identity would have been true REGARDLESS of what you choose for x. (For all x)

Answer 18

Possible solution in this case would be: \(\displaystyle x=45 ^\circ\)
but, if you chose \(\displaystyle x=90 ^\circ\) (for example), then the statement is false.
(This is why it is NOT an identity)

Answer 19

Why would multiplying by cosx cancel out the cscx?

Answer 20

Oh my bad

Answer 21

well, multiply across by sin(x).

Answer 22

same solution, except that I mixed up the sec(x) and csc(x).

Answer 23

Okay, thanks!
One more :) cos^2(2x) - sin^2(2x) = 0

To use the double angle identity on this, would I put it to the fourth power?

Answer 24

FINE I'll open a new question. :D
Thanks everyone for the help!