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Use a half angle formula to fill in the blanks in the identity below

Use a half angle formula to fill in the blanks in the identity below-example-1
User Steinybot
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Recall the identity


\cos^2\Big((\beta)/(2)\Big)=(1+\cos\beta)/(2)

We can rewrite the given equation into


(\cos(5x))^2\Longrightarrow\cos^2\Big(5x\Big)\Longrightarrow\cos^2\Big((10x)/(2)\Big)

Using the identity we get


\begin{gathered} \beta=10x \\ \\ \cos^2\Big((10x)/(2)\Big)=(1+\cos(10x))/(2) \\ \cos^2\Big((10x)/(2)\Big)=(1)/(2)+(1)/(2)\cos(10x) \end{gathered}

Therefore,


(\cos(5x))^2=0.5+0.5\cos(10x)

User Erick Boshoff
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