Question

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

Answer 1

Answer:

It is identity.

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

Step-by-step explanation:

Recall the Pythagorean Identity:

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

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

$\frac{\sin^2(x)}{\cos^2(x)}+\frac{\cos^2(x)}{\cos^2(x)}=\frac{1}{\cos^2(x)}$

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

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