I am running Julia 1.6.7 on a Linux machine and

trying to use the Symbolics.jl package.

Any assistance with the following would be appreciated.

(1) The function simplify() does not simplify the

following trigonometric expression to -1. How can this

simplification be achieved?

julia> y = -(sin(x1t))^2 - (cos(x1t))^2

-(cos(x1(t))^2) - (sin(x1(t))^2)

julia> Symbolics.simplify(y)

-(cos(x1(t))^2) - (sin(x1(t))^2)

(2) The function expand() does not seem to expand

trigonometric functions. Is there a way to achieve

such expansions?

julia> Symbolics.expand(sin(x1t+x2t))

sin(x1(t) + x2(t))

julia> Symbolics.expand(cos(x1t+x2t))

cos(x1(t) + x2(t))

(3) How can irrational values, eg. sqrt(2), exp(1),

etc, be represented and manipulated exactly in

Symbolics.jl?