Minimum value of 5 sin^2 theta + 4 cos^2 thet | vedclass

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(D) Let $f(	heta) = 5 \sin^2 	heta + 4 \cos^2 	heta$.We know that $\sin^2 	heta + \cos^2 	heta = 1$,so $\cos^2 	heta = 1 - \sin^2 	heta$.Substi

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$4$

Vedclass · Answer

(D) Let $f(	heta) = 5 \sin^2 	heta + 4 \cos^2 	heta$.We know that $\sin^2 	heta + \cos^2 	heta = 1$,so $\cos^2 	heta = 1 - \sin^2 	heta$.Substituting this into the expression:$f(	heta) = 5 \sin^2 	heta + 4(1 - \sin^2 	heta)$$f(	heta) = 5 \sin^2 	heta + 4 - 4 \sin^2 	heta$$f(	heta) = \sin^2 	heta + 4$.Since the minimum value of $\sin^2 	heta$ is $0$,the minimum value of $f(	heta)$ is $0 + 4 = 4$.

Minimum value of $5 \sin^2 \theta + 4 \cos^2 \theta$ is

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