 Hello and welcome to the session, let's work out the following question. It says write all the other trigonometric ratios of angle A in terms of secant A. So let's now move on to the solution. First of all, we'll write sin A in terms of secant A. Now sin A can be written as under the root 1- cos A as we know that sin 2 theta plus cos 2 theta is equal to 1. So this implies sin 2 theta is equal to 1- cos 2 theta and this implies sin theta is equal to square root of 1- cos 2 theta. Now cos A can be written as 1 upon secant A. So cos square A is 1 upon secant square A. So this is equal to again, taking as here we have secant square A minus 1 upon secant square A. So this is equal to square root of secant square A minus 1 upon secant A. So sin A is secant square A square root of secant square A minus 1 upon secant A. Now we'll write cos A in terms of secant A cos A is 1 upon secant A. Then we write tan A in terms of secant A. Now tan A is equal to sin A upon cos A. Now sin A from above we have square root of secant square A minus 1 upon secant A into 1 upon cos A. Again this is equal to square root of secant square A minus 1 upon secant A into secant A 1 upon cos A is secant A. Now secant A gets cancelled with secant A and we have tan A is equal to square root of secant square A minus 1. Now we'll write cot A in terms of secant square A. Now cot A can be written as 1 upon tan A. But tan A is secant square A minus 1. So this is equal to 1 upon square root of secant square A minus 1. Now we'll write cos secant A in terms of secant A. Now cos secant A can be written as 1 upon sin A. Now from above we have sin A as square root of secant square A minus 1 upon secant A. This is equal to secant A upon the square root of secant square A minus 1. Hence sin A is equal to square root of secant square A minus 1 upon secant A cos A is equal to 1 upon secant A tan A is equal to square root of secant square A minus 1. We've got A is equal to 1 upon square root of secant square A minus 1. And cos sec A is equal to secant A upon the square root of secant square A minus 1. So this completes the question and the session. Bye for now. Take care. Have a good day.