So, let's use that here.

Namely, this is equal to 1 minus tangent

squared x divided by secant squared x.

And now, let's divide both terms in the numerator by secant squared x,

which gives us 1 divided by secant

squared x minus tangent squared x divided by secant squared x.

And now, let's convert everything to sine and cosine.

In other words, this is equal to 1 over secant x is cosine x, and so,

1 over secant squared x is cosine squared x, and then minus,

now tangent x is sine x over cosine x,

so tangent squared x is sine squared x over cosine squared x,

and secant squared x is 1 over cosine squared x.

Now, what is this simplified to?

Remember, when we divide fractions,

it's the same as multiplying the numerator by the reciprocal of the denominator.

In other words, this is sine squared x divided by cosine squared x,

and then times cosine squared x over 1.

Now, won't these cosine squared x's cancel?

So, all we're left with then is just sine squared x.

That is this is equal to cosine squared x minus sine squared x.

Now, let's recall all the Double Angle Formulas.

Unlike sine and tangent,

cosine has three different double angle formulas.

But if we look at them,

what we just got is equal to the right hand side of the first one,

which means that what we just got is equal to cosine of 2x.

So, this is equal to

cosine 2x which is our left hand side.

And so, we verified this identity.

And this is how we verify a trig identities that involve the Double Angle Formulas.

Thank you, and we'll see you next time.