sin 4a = 2(sin 2a)(cos ) = 2(2 sin a cos a)(cos² a - ) = 4 sin a cos³ a - 4 sin³ a cos a
sin 4a = 2(sin 2a)(cos ) = 2(2 sin a cos a)(cos² a - ) = 4 sin a cos³ a - 4 sin³ a cos a
Answer
Explanation:
Step1: Use double - angle formula for sine
The double - angle formula for sine is $\sin 2\alpha=2\sin\alpha\cos\alpha$. Let $\alpha = 2A$, then $\sin4A = 2\sin2A\cos2A$. So the first blank is $2A$.
Step2: Use double - angle formula for cosine
The double - angle formula for cosine is $\cos2A=\cos^{2}A-\sin^{2}A$. So the second blank is $\sin^{2}A$.
Answer:
First blank: $2A$ Second blank: $\sin^{2}A$