Express sin32+sin54 as sum or difference.

Hello!
This expression is already a sum of two numbers, sin(32) and sin(54). Probably you want or express it as a product, or as an expression involving trigonometric functions of sum or difference of the arguments, 32 and 54.
For this, we need the well-known formula
sin(x) + sin(y) = 2sin((x+y)/2)cos((x-y)/2),
which is true for any real x and y.
For the given numbers it gives us
sin(32) + sin(54) = 2sin((32+54)/2)cos((32-54)/2) =
= 2sin(43)cos(-11) = 2sin(43)cos(11).
 
If you misspelled the expression, and it is actually sin(32)*sin(54), then we really can express it as a sum with the help of the formula
sin(x)sin(y) = 1/2(cos(x-y)-cos(x+y)),
for the given numbers it is
sin(32)sin(54) = 1/2(cos(-22)-cos(86)) = 1/2(cos(22)-cos(86)).
 
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