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Answer:
-sin(4a)
Step-by-step explanation:
The factors can be simplified as follows:
sin(3π/2 -a) = -cos(a)
cos(π/2 +a) = -sin(a)
cos(π +2a) = -cos(2a)
Then the product can be written ...
y = 4sin(3π/2 -a)· cos(π/2 +a)·cos(π +2a) = 2(2(-cos(a))(-sin(a))·(-cos(2a))
Using the relation ...
sin(2a) = 2sin(a)cos(a), we get ...
y = 2(sin(2a)(-cos(2a)) = -2sin(2a)cos(2a)
y = -sin(4a)
The simplified expression is -sin(4a).
