Question

if y=4/(sin theta+ cos theta) then minimum value of y is?

Answer 1

The minimum value of y is "2√2".

Explanation:

In the function value of y the dividing term, should only be minimal, if the denominator is maximal for numerator, so(\sin \theta + cos\theta) must be maximum, which would be the case:

$\to \frac{d}{d\theta}(\sin \theta+\cos \theta)=0$

$\to \frac{d}{d\theta}\sin \theta+\frac{d}{d\theta}\cos \theta=0\\\\\to \cos \theta- \sin \theta=0\\\\\to \cos \theta=\sin \theta\\\\ \to\frac{\sin \theta}{\cos \theta}=1\\\\ \to \tan \theta =1\\\\\to \tan \theta = \tan 45^{\circ}\\\\\to \theta= 45^{\circ}$

Put the $\theta$ value in function y or in given equation:

$\to y=\frac{4}{\sin \theta+\cos \theta}$

      $= \frac{4}{\sin 45^{\circ}+\cos 45^{\circ}}\\\\= \frac{4}{\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}}\\\\= \frac{4}{\frac{1+1}{\sqrt{2}}}\\\\= \frac{4}{\frac{2}{\sqrt{2}}}\\\\= \frac{4}{2}\times \frac{\sqrt{2}}{1}\\\\= \frac{2}{1}\times \frac{\sqrt{2}}{1}\\\\= 2\sqrt{2}$

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• Minimum value: https://brainly.in/question/4391573

Answer 2

Answer:

2✓2

Explanation:

substitute value of theta 45° as while differentiating Dy/dtheta we get tan theta=1

so value of theta is 45°....