The minimum value of 5 sin^2 theta + 4 cos^2 | vedclass

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(D) Let $f(	heta) = 5 \sin^2 	heta + 4 \cos^2 	heta$. Using the identity $\sin^2 	heta + \cos^2 	heta = 1$,we can write $\cos^2 	heta = 1 - \sin

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) Let $f(	heta) = 5 \sin^2 	heta + 4 \cos^2 	heta$. Using the identity $\sin^2 	heta + \cos^2 	heta = 1$,we can write $\cos^2 	heta = 1 - \sin^2 	heta$. Substituting this into the expression: $f(	heta) = 5 \sin^2 	heta + 4(1 - \sin^2 	heta)$ $f(	heta) = 5 \sin^2 	heta + 4 - 4 \sin^2 	heta$ $f(	heta) = 4 + \sin^2 	heta$. Since the minimum value of $\sin^2 	heta$ is $0$,the minimum value of $f(	heta)$ is $4 + 0 = 4$.

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

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