 Hello friends, welcome to the session I am Malka. Let's discuss find dy by dx if y equal to 12 into 1 minus cos t x equal to 10 into t minus sin t where minus pi by 2 is less than t is less than pi by 2. So let's start with the solution. We are given y equal to 12 into 1 minus cos t and x equal to 10 into t minus sin t. Let's differentiate both sides with respect to t we get dy upon dt equal to 12 sin t dx upon dt equal to 10 into 1 minus cos t. Now, by chain rule that is dy upon dx equal to dy upon dt into dt upon dx we get dy upon dt is 12 sin t upon 10 into 1 minus cos t. Now, on cancelling 12 and 10 we get 6 and 5 and further we will substitute the value of sin t which is 2 sin t by 2 cos t by 2 upon 5 into 2 sin square t by 2. This implies dy by dx equal to 6 upon 5 into 2 to cancel out sin sin cancel out we are left with cos t by 2 upon sin t by 2. This implies dy upon dx equal to 6 upon 5 cot t by 2. Therefore, dy upon dx equal to 6 upon 5 cot t by 2. Hope you understood the solution and enjoyed the session goodbye and