Cotangent

It was cotangent of 2x over the cosecant of x.

And tangent is sine over cosine, so cotangent's the opposite.

One. You could just look at do the tangent because that involves the opposite over the adjacent.

And cotangent of 2x is equal to 1 over tangent of 2x.

You would have thought that the cosecant is 1 over cosine.

Cos

Cosh

Hyperbolic cosine

Arc cosine

It's cosine.

So I'm just going to write my cosine of t first.

Inverse hyperbolic cosine

Cosine to the fifth of x.

Hyperbolic cosine

That's the cosine of x.

Cosine of x becomes u.

So it's 5 cosine to the fourth of x.

It's cosine of x.

Cosine of x d of x.

So now this integral becomes and the denominator, instead of cosine of x squared, u is cosine of x.

We're left with the limit as x approaches 0 of cosine of 2x over 2 cosine of x.

But when the marriage was about to be consummated,

That's equal to sine over cosine divided by sine.

So the derivative of g of x is cosine of x.

It was the antiderivative of cosine of x.

Well, cosine is adjacent over hypotenuse.

Well the derivative of sine of x is just cosine of x. So it's going to be negative 2 cosine of x.

So if u is equal to cosine of x, this thing is equal to 1 over cosine of x plus c is equal to the antiderivative of our original problem, which was sin of x over cosine of x squared dx.

That will be equal to cosine of whatever is in front of the i, so cosine of mu x plus i sine of mu x.

Well, it's just cosine of x.

Again cosine is adjacent over hypotenuse

Well, yeah, it's just cosine of x.

All of that over cosine of x squared.

This means cosine of x to the fifth.

Soh cah toa, cos is adjacent over hypotenuse

What's cosine of 90 degrees?

What's the derivative of cosine of x?

This is just what sine, cosine, and tangent are.

Well, tangent is just sine over cosine.

And then we have minus cosine of t.

So it's cosine squared of tau, and then minus let's rewrite the cosine of t first, and I'm doing that because we're integrating with respect to tau.

And let's say g of x is cosine of x, right?

I'm sorry, g prime of x is cosine of x.

Cosine of minus theta is equal to cosine of theta.