The exact value of cos^2 73^circ + cos^2 47^c | vedclass

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(C) Let $E = \cos^2 73^\circ + \cos^2 47^\circ + \cos 73^\circ \cos 47^\circ$. Using the identity $\cos^2 	heta = \frac{1 + \cos 2	heta}{2}$ and $2

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$3/4$

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(C) Let $E = \cos^2 73^\circ + \cos^2 47^\circ + \cos 73^\circ \cos 47^\circ$. Using the identity $\cos^2 	heta = \frac{1 + \cos 2	heta}{2}$ and $2 \cos A \cos B = \cos(A+B) + \cos(A-B)$: $E = \frac{1 + \cos 146^\circ}{2} + \frac{1 + \cos 94^\circ}{2} + \frac{\cos 120^\circ + \cos 26^\circ}{2}$ $E = \frac{1}{2} + \frac{\cos 146^\circ}{2} + \frac{1}{2} + \frac{\cos 94^\circ}{2} + \frac{-1/2}{2} + \frac{\cos 26^\circ}{2}$ $E = 1 - \frac{1}{4} + \frac{1}{2} (\cos 146^\circ + \cos 94^\circ + \cos 26^\circ)$ Since $\cos 146^\circ + \cos 94^\circ = 2 \cos(\frac{146+94}{2}) \cos(\frac{146-94}{2}) = 2 \cos 120^\circ \cos 26^\circ = 2(-1/2) \cos 26^\circ = -\cos 26^\circ$. $E = \frac{3}{4} + \frac{1}{2} (-\cos 26^\circ + \cos 26^\circ) = \frac{3}{4}$.

The exact value of $\cos^2 73^\circ + \cos^2 47^\circ + (\cos 73^\circ \cdot \cos 47^\circ)$ is

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