 Hi and welcome to the session, I am Deepika here. Let's discuss a question. In triangle A, B, C, right angle at B, if tan A is equal to 1 over root 3, find the value of part 1, sin A cos C plus cos A sin C, part 2, cos A cos C minus sin A sin C. Now we know that in the right angle triangle A, B, C, according to the Pythagoras theorem, hypotenuse here is equal to some of the squares of target two sides, that is, is equal to A B square plus B C square and is equal to opposite to the acute angle A, that is, B C upon hypotenuse A C and cos A is equal to sin adjacent to acute angle A, that is, A B upon hypotenuse A C. Similarly, sin C is equal to sin opposite to angle C, that is, A B upon hypotenuse and sin adjacent to angle C upon hypotenuse, that is, B C upon A C. So, this is a key idea for the given question. We will take the help of this key idea to solve up our question. So, let's start the solution. Solution part 1 is equal to 1 over root 3 to angle A is equal to B C upon 1 over root 3. So, therefore, a positive number. According to the Pythagoras theorem, A square is equal to A B square plus B C square. Therefore, A C square is equal to C, that is, X upon equal to 1 over root 3 is equal to 3 upon A C, that is, root 3X upon 2X and this is equal to root 3 upon 2 and similarly is equal to B C upon A C, that is, root 3X upon 2X and this is equal to root 3 upon 2 and cos C is equal to B C upon A C and which is equal to X upon 1 by 2. So, our given question is we have to find the value of sin A cos C and substituting the values of cos C plus cos A sin C 1 by 2. So, this is equal to 1 by 2 into cos C. Cos C is our 1 by 2 plus cos A, this is root 3 by 2 which is again root 3 by 2 is equal to 1 by 4 plus 3 by 4 and this is equal to this is equal to 1. Hence, the answer for part 1 is 1. Solution of part 2, putting the values of cos A sin C cos C in minus sin A sin C is equal to now our cos A is equal to root 3 by 2 is equal to 1 by 2. So, we get root 3 by 2 into 1 by 2 minus now sin A is 1 by 2 and sin C is root 3 by 2. This is 1 by 2 into root 3 by 2. So, this is equal to root 3 by 4 minus root 3 by 4 and this is equal to 0. Hence, the answer for part 2 is 0. I hope the solution is clear to you. Bye and take care.