Use Maple to find the identities for sinx+y and cosx−y and check the results.
The Context Panel options Expand and Combine≻trig give the following solution.
sinx+y= expand sin⁡x⁢cos⁡y+cos⁡x⁢sin⁡y= combine sin⁡x+y
cosx−y= expand cos⁡x⁢cos⁡y+sin⁡x⁢sin⁡y= combine cos⁡x−y
Apply the expand and combine commands.
Maple also knows the Pythagorean identities and the multiple-angle formulas, which are available through the Context Panel options Simplify, Expand, and Combine, or the simplify, expand, and combine commands. Maple uses cosx as much as possible, as for example, in
sin4 x cos3 x= simplify trig 4⁢sin⁡x⁢cos⁡x2⁢8⁢cos⁡x4−10⁢cos⁡x2+3→assign to a nameq
Use the simplify command with the indicated syntax to force the use of sinx.
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