Standard is to write "exponents" as "^(-1)". Although, strictly speaking, the "-1" here is not an "exponent"- sin^(-1)(x) is the inverse function, the funct, v, such that f(sin^(-)(x))= sin^(-1)(f(x))= x, not 1/sin(x).
This problem would be easy if it were just "cos(sin^(-1)(x))" because, for any u, cos(u)= sqrt(1- sin^2(u)) so that cos(sin^(-1)(x))= sqrt(1- (sin(sin^(-1)(x))^2)= sqrt(1- x^2) because, of course, sin(sin^(-1)(x))= x.
So, do you know any ways to simplify cos(a- b) into functions of a and b separately?
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