For all values of theta,the values of 3-cos t | vedclass

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(A) Let $f(	heta) = 3-\cos 	heta+\cos \left(	heta+\frac{\pi}{3}ight)$.Using the identity $\cos(A+B) = \cos A \cos B - \sin A \sin B$:$f(	heta) =

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$[2,4]$

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(A) Let $f(	heta) = 3-\cos 	heta+\cos \left(	heta+\frac{\pi}{3}ight)$.Using the identity $\cos(A+B) = \cos A \cos B - \sin A \sin B$:$f(	heta) = 3-\cos 	heta + \left(\cos 	heta \cdot \cos \frac{\pi}{3} - \sin 	heta \cdot \sin \frac{\pi}{3}ight)$$f(	heta) = 3-\cos 	heta + \frac{1}{2} \cos 	heta - \frac{\sqrt{3}}{2} \sin 	heta$$f(	heta) = 3 - \frac{1}{2} \cos 	heta - \frac{\sqrt{3}}{2} \sin 	heta$$f(	heta) = 3 - \left(\cos 	heta \cdot \cos \frac{\pi}{3} + \sin 	heta \cdot \sin \frac{\pi}{3}ight)$$f(	heta) = 3 - \cos \left(	heta - \frac{\pi}{3}ight)$Since $-1 \leq \cos \left(	heta - \frac{\pi}{3}ight) \leq 1$,$3 - (1) \leq f(	heta) \leq 3 - (-1)$$2 \leq f(	heta) \leq 4$.Thus,the interval is $[2,4]$.

For all values of $\theta$,the values of $3-\cos \theta+\cos \left(\theta+\frac{\pi}{3}\right)$ lie in the interval :

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