To change the sum into a product, the given expression has
to have 2 like trigonometric functions.
Since we have
already the term sin a, we'll write the value 1 as sin
pi/2.
We'll re-write the
expression:
sin a + sin
p/2
To change the sum into a product we'll apply the
formula:
sin a + sin b =
2sin[(a+b)/2]cos[(a-b)/2]
We'll let a = a and b =
pi/2:
sin a + sin pi/2 =
2sin[(2a+pi)/4]cos[(2a-pi)/4]
sin a + sin pi/2 = 2sin[(a/2
+ pi/4)]cos[(a/2 -pi/4)]
sin a + 1 =
2sin[(a/2 + pi/4)]cos[(a/2 -pi/4)]
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