 Hello and welcome to the session. Let us discuss the following question. Question says show that cos 38 degrees multiplied by cos 52 degrees minus sin 38 degrees multiplied by sin 52 degrees is equal to 0. First of all let us understand that if in any right angle theta is any of the acute angles then cos 90 minus theta is equal to sin theta. This is the k idea to solve the given question. Now let us start the solution. We have to show that cos 38 degrees multiplied by cos 52 degrees minus sin 38 degrees multiplied by sin 52 degrees is equal to 0. First of all let us solve left hand side of this expression. Left hand side of this expression is cos 38 degrees multiplied by cos 52 degrees minus sin 38 degrees multiplied by sin 52 degrees. Now we know 38 degrees and 52 degrees are complementary angles. So complement of 32 degrees is 52 degrees and complement of 52 degrees is 38 degrees. Now we can write cos 38 degrees is equal to cos 90 minus 52 degrees cos 52 degrees can be written as cos 90 degrees minus 38 degrees minus sin 38 degrees multiplied by sin 52 degrees. Now using k idea we know cos 90 minus theta is equal to sin theta. Here value of theta is 52 degrees. So we can write cos 90 minus 52 degrees is equal to sin 52 degrees multiplied by here cos 90 minus 38 degrees is equal to sin 38 degrees minus sin 38 degrees multiplied by sin 52 degrees. Now we know multiplication is commutative. So sin 52 degrees multiplied by sin 38 degrees is equal to sin 38 degrees multiplied by sin 52 degrees minus sin 38 degrees multiplied by sin 52 degrees. Now subtracting these two terms we get 0. Now clearly we can see left hand side is equal to 0 which is further equal to right hand side. So we get cos 38 degrees multiplied by cos 52 degrees minus sin 38 degrees multiplied by sin 52 degrees is equal to 0. So this is our required answer. Hence proved this completes the session. Hope you understood the session. Take care and have a nice day.