We have to prove that tan theta plus cot theta is equal to sec theta times cosec theta.

First, we will take the left-hand side.
The left-hand side is tan theta plus cot theta.

Now, we will change both into sine and cosine.
So, tan theta is sine theta divided by cosine theta,
and cot theta is cosine theta divided by sine theta.

Now, add them:
sine theta divided by cosine theta plus cosine theta divided by sine theta.

To add these, take the same denominator.
The common denominator is sine theta multiplied by cosine theta.

Now, write:
sine squared theta plus cosine squared theta divided by sine theta multiplied by cosine theta.

We know that sine squared theta plus cosine squared theta is equal to 1.

So, the left-hand side becomes:
1 divided by sine theta multiplied by cosine theta.

Now, take the right-hand side.
The right-hand side is sec theta times cosec theta.

Change both into sine and cosine.

Sec theta is 1 divided by cosine theta,
and cosec theta is 1 divided by sine theta.

Now multiply them:
1 divided by sine theta multiplied by cosine theta.

So, left-hand side and right-hand side are equal.

Therefore, the given equation is proved.

Hence proved.