how an identity is a special case of an equation ?

Question

ben00 · Answer

What kind of equation?

kainui · Answer

Do you mean:

$$x=x$$

abdullahm · Answer

(I'm sorry. I don't see a way how I can guide the user, so I'm trying to explain it to him. This is not meant to be a direct amswer.)

An identity is a special kind of equation because no matter what numbers you plug in, you will always get a term.

For example, sin^2 (x) + cos^2 (x) = 1.

If you look at a right angle triangle and label all the sides (a, b, and c), and label an angle x. And we find the sin and cos in relation to the sides, this is what happens:

Now, the right angle was labeled c on the hypotension and a and b on the 2 legs.

(a/c)^2 + (b/c)^2 = 1

a^2/c^2 + b^2/c^2 = 1

(a^2 + b^2)/c^2 = 1

Now, the sum of the squares of the kegs is c^2 using the Pythagorean Theorem.

c^2/c^2 = 1

1 = 1

So, you can see that for any value you plug in, you should always end up with 1. 


Do you understand/know how to answer your question now?

skullpatrol · Answer

An identity is an equation that is true for every value of the variable (or variables). 

Some equations may have no solution because there is no value of
the variable that will result in a true equation. For example, x + 1 = x + 2
has no solution; it cannot be true. An equation that is true for every value of
the variable is called an identity . For example, x + x = 2x is true for every
value of x.

jiteshmeghwal9 · Answer

Thanx to all of u :)

specially @skullpatrol & @AbdullahM

skullpatrol · Answer

Thanks for asking a great question :-)

abdullahm · Answer

It was my pleasure! :-)