The minimum value of 2 sin ^{2} theta+3 cos ^ | vedclass

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Question

(C) Given expression: $2 \sin ^{2} 	heta + 3 \cos ^{2} 	heta$We know that $\sin ^{2} 	heta = 1 - \cos ^{2} 	heta$.Substituting this into the expre

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$2$

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(C) Given expression: $2 \sin ^{2} 	heta + 3 \cos ^{2} 	heta$We know that $\sin ^{2} 	heta = 1 - \cos ^{2} 	heta$.Substituting this into the expression:$2(1 - \cos ^{2} 	heta) + 3 \cos ^{2} 	heta$$= 2 - 2 \cos ^{2} 	heta + 3 \cos ^{2} 	heta$$= \cos ^{2} 	heta + 2$Since the range of $\cos ^{2} 	heta$ is $[0, 1]$,the minimum value of $\cos ^{2} 	heta$ is $0$.Therefore,the minimum value of the expression is $0 + 2 = 2$.

The minimum value of $2 \sin ^{2} \theta+3 \cos ^{2} \theta$ is

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