 Hello and welcome to the session. I am Arsha and I am going to help you with the following problem that says proof that 2 sin square 3 pi upon 4 plus 2 cos square pi upon 4 plus 2 sin square pi upon 3 is equal to 10. There is no million method solution and we will evaluate the value of left hand side and show that its value is equal to 10. The left hand side is 2 sin square 3 pi upon 4 plus 2 cos square pi upon 4 plus 2 sin square pi upon 3 which can further be written as 2 sin 3 pi upon 4 whole square plus 2 cos pi upon 4 whole square plus 2 times sin pi upon 3 whole square. This can further be written as 2 times of sin 3 pi upon 4 can be written as pi minus pi upon 4 whole square plus 2 times cos pi upon 4 whole square plus 2 times sin pi upon 3 whole square which is further equal to 2 sin pi upon 4 whole square since pi minus pi by 4 lies in the second quadrant and in the second quadrant sin function is positive plus 2 times of cos pi by 4 whole square plus 2 times say pi upon 3 whole square which is further equal to 2 times sin pi by 4 sin 45 degree which is 1 upon root 2 nvm whole square plus 2 times cos pi by 4 is again 1 upon root 2 whole square plus 2 times say pi upon 3 is 2 whole square which is further equal to 2 upon 2 plus 2 upon 2 plus 2 into 4 which is further equal to 1 plus 1 plus 8 which is further equal to 10 which is the right hand side of the given equation. So, we have left hand side is equal to right hand side and thus n square 3 pi upon 4 plus 2 cos square pi upon 4 plus 2 sin square pi upon 3 is equal to 10. So, this completes the solution hope you enjoyed it take care and have a good day.