 Hello and welcome to the session. Let us understand the following question today. If x and y are connected parametrically by the questions given below, without telling me letting the parameter with find d y by dx, we have x is equal to a cos t plus log tan t by 2 and y is equal to a sin t. Now, let us write the solution given to us as x is equal to a cos t plus log of tan t by 2 and y is equal to a sin t. Now, consider x is equal to a multiplied by cos t plus log of tan t by 2. Therefore, dx by dt is equal to a multiplied by minus sin t plus 1 by tan t by 2 multiplied by sex square t by 2 multiplied by 1 by 2, which is equal to a multiplied by minus sin t plus this can be written as cos t by 2 by sin t by 2 multiplied by 1 by cos square t by 2 multiplied by half. Now, we see that this cos t by 2 gets cancelled by cos t by 2. So, we get a multiplied by minus sin t plus 1 by 2 sin t by 2 cos t by 2, which is equal to a multiplied by minus sin t plus 1 by sin t, which is equal to a multiplied by now taking LCM sin t, we get minus sin square t plus 1 in numerator. So, which is equal to a 1 minus sin square t is equal to cos square t upon sin t. Now, consider y is equal to a sin t. Therefore, dy by dt is equal to a cos t. Now, by chain rule, dy by dx is equal to dy by dt multiplied by dt by dx, which is equal to dy by dt is equal to a cos t multiplied by dt by dx is equal to inverse of dx by dt multiplied by 1 by a sin t by cos square t. So, we see that this a and a gets cancelled and 1 cos t gets cancelled with cos t. So, we are left with sin t by cos t, which is equal to tan t and our required dy by dx. Hence, the required answer is tan t. I hope you understood the question. Bye and have a nice day.