 Hello friends, let's work out the following question. It says express trigonometric ratios sin a secant a tan a in terms of cot a. So let's now move on to the solution. Now first of all we'll express sin a in terms of cot a. Now sin a can be written as 1 upon cos secant a. Right, now we know that cos secant square theta minus cot square theta is equal to 1. So this implies cos secant square theta is equal to 1 plus cot square theta. So this implies cos secant theta is equal to the square root of 1 plus cot square theta. Right, so now here 1 upon cos secant a can be written as under the root of 1 upon under the root of 1 plus cot square a. Now we'll express secant a in terms of cot a. Now secant a can be written as 1 upon cos a or we can do it directly. Secant a can be written as square root of 1 plus tan square a. As we know that secant square theta minus tan square theta is equal to 1. So this implies secant square theta is equal to 1 plus tan square theta and this implies secant theta is equal to under the root of 1 plus tan square theta. Now we have to express this in terms of cot theta, cot a that is. Now tan square a can be written as 1 upon cot square a because tan theta is equal to 1 upon cot theta. So this becomes taking calcium we have cot square a plus 1 upon cot square a. So this is equal to cot square a plus 1 upon cot a. Now we'll express tan a in terms of cot a. Now we have already discussed that tan theta is equal to 1 over cot theta so tan a is equal to 1 over cot k. Hence the answer to the first part that is sin a is equal to 1 upon under the root 1 plus cot square a is equal to 1 over cot a and secant a is equal to under the root 1 plus cot square a upon cot a. So this completes the question on this session. Bye for now. Take care. Have a good day.