cos ^2 45^{circ}+cos ^2 135^{circ}+cos ^2 225 | vedclass

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(B) We use the property $\cos^2 	heta = \cos^2(180^{\circ} \pm 	heta) = \cos^2(360^{\circ} \pm 	heta)$.$\cos 135^{\circ} = \cos(180^{\circ} - 45^{\

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) We use the property $\cos^2 	heta = \cos^2(180^{\circ} \pm 	heta) = \cos^2(360^{\circ} \pm 	heta)$.$\cos 135^{\circ} = \cos(180^{\circ} - 45^{\circ}) = -\cos 45^{\circ} \implies \cos^2 135^{\circ} = \cos^2 45^{\circ}$.$\cos 225^{\circ} = \cos(180^{\circ} + 45^{\circ}) = -\cos 45^{\circ} \implies \cos^2 225^{\circ} = \cos^2 45^{\circ}$.$\cos 315^{\circ} = \cos(360^{\circ} - 45^{\circ}) = \cos 45^{\circ} \implies \cos^2 315^{\circ} = \cos^2 45^{\circ}$.Thus,the expression becomes:$\cos^2 45^{\circ} + \cos^2 45^{\circ} + \cos^2 45^{\circ} + \cos^2 45^{\circ} = 4 \cos^2 45^{\circ}$.Since $\cos 45^{\circ} = \frac{1}{\sqrt{2}}$,we have $\cos^2 45^{\circ} = \frac{1}{2}$.Therefore,$4 	imes \frac{1}{2} = 2$.

$\cos ^2 45^{\circ}+\cos ^2 135^{\circ}+\cos ^2 225^{\circ}+\cos ^2 315^{\circ} = $

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