Performing Sum to Product identity of trigonometric functions

[amindanial]

How can I perform sum to product identity of trigonometric functions on HP prime as follows:
sin(a)+sin(b) to get 2sin((a+b)/2)cos((a-b)/2).

[Jan 11]

Now in HP Prime, you won't be able to perform this trigonometric identity. Maybe, in a future update, such a function will be added.

[amindanial]

(12-24-2024 03:15 PM)Jan 11 Wrote:  Now in HP Prime, you won't be able to perform this trigonometric identity. Maybe, in a future update, such a function will be added.

Thetefore, we have to inform the company about adding this function in the next update.

[Thomas Klemm]

Meanwhile with my HP-48GX I can define:

Code:

DIR
  EXPR 'SIN(U+V)+SIN(U-V)'
  ∑→Π
    « {
        'SIN(&A)+SIN(&B)'
        '2*SIN((&A+&B)/2)*COS((&A-&B)/2)'
      } ↓MATCH
    »
END

And then run:

EXPR ∑→Π DROP COLCT COLCT

This results in:

'2*SIN(U)*COS(V)'

[Albert Chan]

XCas has trigsimplify, but we had to nudge it to get what we want.

XCas> m := sin(a) + sin(b)
XCas> trigsimplify( m(a=c+g, b=c-g) ) (c=(a+b)/2, g=(a-b)/2)

2 * cos((a-b)/2) * sin((a+b)/2)

XCas> tlin( ans() )

sin(a) + sin(b)

[amindanial]

I think CAS engine of HP prime has to be upgraded.