Is $tan^2x -= sec^2x - 1$ an identity?

Question

169345 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-09T17:10:50

True

Start with the well known pythagorean identity:

$sin^2x + cos^2x -= 1$

This is readily derived directly from the definition of the basic trigonometric functions $sin$ and $cos$ and Pythagoras's Theorem.

Divide both side by $cos^2x$ and we get:

$sin^2x/cos^2x + cos^2x/cos^2x -= 1/cos^2x$

$:. tan^2x + 1 -= sec^2x$

$:. tan^2x -= sec^2x - 1$

Confirming that the result is an identity.

Answer 2 · 2018-01-09T17:12:45

Yes, $sec^2-1=tan^2x$ is an identity.

We start from $sin^2x+cos^2x=1$ .

Then divide everything by $cos^2x$

$sin^2x/cos^2x+cos^2x/cos^2x=tan^2x+1=1/cos^2x=sec^2x$

Rearrange to find $tan^2x$

$tan^2x=sec^2x-1$

Is tan^2x -= sec^2x - 1tan^2x -= sec^2x - 1 an identity?