Question

Please help me
-tan^2 x+sec^2 x=1

Answer 1

It is identity.

It is true for any x in the domain of the equation.

Explanation:

Recall the Pythagorean Identity:

`\sin^2(x)+\cos^2(x)=1`.

Divide both sides be
`\cos^2(x)`:

`(\sin^2(x))/(\cos^2(x))+(\cos^2(x))/(\cos^2(x))=(1)/(\cos^2(x))`

`\tan^2(x)+1=\sec^2(x)`.

`\tan^2(x)+1=\sec^2(x)` is also known as a Pythagorean Identity as well.

I'm going to apply this last identity I wrote to your equation on the left hand side.

Replacing
`\sec^2(x)` with
`\tan^2(x)+1`:

`-\tan^2(x)+[\tan^2(x)+1]`

Distribute:

`-\tan^2(x)+\tan^2(x)+1`

Combine like terms:

`0+1`

`1`

This is what we also have on the right hand side so we have confirmed your given equation is an identity.