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

Question

asked Nov 9, 2020 198k views

1 Answer

Alex Chengalan · Answer 1 · 2020-11-15T16:13:07+0000

Answer:

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

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