00:01
So in the given question what we have is we have a function f of x which is given as in the form of a matrix pos x minus sine x, sine x and cos x.
00:19
So this is what is given and we are told to find f of x plus y minus f f of x plus y minus f of x x times f of y f of x times f of y so this is what we need to find so what we are we are having in the question as options is option a which is null matrix option b which is saying that the given expression would give us a unit matrix option c says that it would be a scalar matrix and option d says that it would be none of this.
01:13
So what can we do over here? so first what we are going to do is we can take the product f of x times f of y, right? so f of x, f of x times f of y can be found as minus cos x minus x, it is not minus coxx, it is just cos x, right? so it is goss x and minus sine x and in the second row we have sine x, and for f of y we we would have cos y minus sine y, sine y, sine y, cost y.
02:07
And when we multiply this, what we would get is, we would have cost x, cosy, minus sine x, sine y.
02:24
And then we have minus cos x, minus cos x, sine y...