 hello friends so welcome to another demonstration video on trigonometry so in this case we are going to show that the three identities namely sin square theta plus cos square theta equals to one cosine square theta minus cot square theta is also one and secant square theta minus tan square theta is one so we are going to demonstrate how you know for every angle so it is independent of the angle chosen and it is always going to be one so what I'm going to do is I am going to start from let us say the value of theta to be zero can you see now the the value of theta is zero so in this case also you know we are seeing it is one all all the three identities if you can see now I am going to increase the value of theta so you can see the theta value is changing but the identity is same as in the value of the the two terms some of the two terms is not going to change and it is not changing also so if you see as I am increasing the theta value there is no impact on the right hand side it is always one though the individual terms are changing but the total sum of the two terms is always always one so this is now when theta is 90 degree it's again you know so here at theta actually tan theta is not defined so here the identity also will not be defined so hence barring those values of theta where the trigonometric ratio is not defined everywhere else you can see now I am in the second quadrant second quadrant also the value remains the same and now as I will switch over to the third quadrant it will stay the same so you can see at any given value of theta the three identities the total sum is not going to change right so sin square theta is sin square theta plus cos square theta is always going to be one cosecant square theta minus cot square theta is always going to be one and secant square theta minus tan square theta is always going to be one so I am going to show you some standard values like 30 degrees and all so this is almost 30 degrees now yes so this is 30 degrees 30.04 almost 30 degrees all let us say when we are going towards 45 degrees so yes so almost 45 degrees right so 44.96 is almost 45 degrees so here you can see it doesn't anyways it doesn't depend on the value of the angle so hence at any given angle you see the values remain the same hence trigonometric identities because trigonometric identity is an equation where the this equation holds for any value of the angle or the variable in this case is the angle so hence any value of the variable right that's what so this session was to demonstrate the three identities that indeed it doesn't depend on any of the value of the angle thank you