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Q.
The least value of $2\,\sin^2\theta+3\,\cos^2\theta$ is
Application of Derivatives
Solution:
$2\,sin^{2}\,\theta+3\,cos^{2}\,\theta$
$=2\left(sin^{2}\,\theta+cos^{2}\,\theta\right)+cos^{2}\,\theta$
$=2+cos^{2}\,\theta$
Least value of $cos^{2}\,\theta=0$
$\therefore $ least value of $25\, sin^{2}\,\theta+3\,cos^{2}\,\theta$
$=2+0=2$