 Hello and welcome to the session. Let us understand the following question today. If x and y are connected parametrically by the equations given below, without eliminating the parameter find d y by dx, we have x is equal to sin t and y is equal to cos 2t. Now let us write the solution. Given to us is x is equal to sin t and y is equal to cos 2t. Therefore, dx by dt is equal to cos t and dy by dt is equal to minus 2 sin 2t. Therefore, 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 minus 2 sin 2t multiplied by dt by dx is equal to 1 by cos t, which is equal to minus 2 multiplied by sin 2t is equal to 2 sin t cos t multiplied by cos t. Now here we see that this cos t and cos t gets cancels. So it is equal to minus 4 sin t. Hence, minus 4 sin t is our required answer. I hope you understood the question. Bye and have a nice day.