Question

By graphing both sides of the equation, determine whether the following is an identity:

1+sec^2x= tan^2 x

Answer 1

Graphing is overkill... Let
`x=0`. Then
`\sec0=1`, while
`\tan0=0`. But
`1+1=2\\eq0`, so this is not an identity.

Answer 2

It is not an identity

Explanation:

If you graphic the two equations (left and right) separately, if they are an identity, they will be the same graphic, which is not true in this case.

Another way in order to know if an equation is an identity, you can replace some values ​​at x, for example 2 values:

X=30

X=60

And now we substitute in the equation, like this:

`1+sec^2(30)=tan^2(30)`

2,33=0,33 this is not equal on both sides

`1+sec^2(60)=tan^2(60)`

5=3 this is not equal on both sides

And if the results for each number x are the same on both sides of the equation, it is an identity. In this case they are different.