A) \[cos\text{ }2A\]
B) \[sin\text{ }3A\]
C) \[sin\text{ }2A\]
D) \[cos\text{ }4A\]
E) \[sin\text{ }4A\]
Correct Answer: E
Solution :
\[4\text{ }sin\text{ }A\text{ }co{{s}^{3}}A-4\text{ }cos\text{ }A\text{ }si{{n}^{3}}\text{ }A\] \[=4\text{ }sin\text{ }A\text{ }cos\text{ }A\text{ }(co{{s}^{2}}A-si{{n}^{2}}A)\] \[=2\text{ }sin\text{ }2A\text{ }cos\text{ }2A=sin\text{ }4A\]
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