Question

Find maximum value of Expression.

sinѲ + cosѲ = 0

Answer 1

Required Answer :

• cos θ = 0 when θ = 90 ˚ ,

• 270˚ . Maximum value of cos θ is 1

when θ = 0 ˚, 360˚.

Hope it clears ur doubts.

Answer 2

$\underline{\boxed{\bold{Question}}}$

↠  Find maximum value of Expression E = sinθ + cosθ = 0

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$\underline{\boxed{\bold{Important\; Information}}}$

↠ To find the maximum value of the expression, we usually differentiate the given expression with respect to the variable present in it and then equating it to zero(0).

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Mathematically,

Let y be function of x

→ y = f(x)  

Differentiating with respect to x,

$:\implies \frac{dy}{dx} = \frac{d(f(x))}{dx} = 0$

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$\underline{\boxed{\bold{Answer}}}$

Let's Start !

E = sinθ + cosθ

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Here variable is "θ". So we will differentiate with respect to "dθ".

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$:\implies \frac{d(E)}{d\theta} = \frac{(sin\theta + cos\theta)}{d\theta} = 0$

$:\implies \frac{d(E)}{d\theta} = cos\theta - sin\theta = 0$

$:\implies cos\theta = sin\theta$

$:\implies cos\theta = cos(90^{\circ} - \theta)$

$:\implies \theta = 90^{\circ} - \theta$

$:\implies \theta = 45^{\circ}$

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∴ Expression will have maximum value at θ = 45°

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Now substituting θ = 45° in the expression.

$:\implies E = sin\theta + cos\theta$

$:\implies E = sin(45^{\circ})+ cos(45^{\circ})$

$:\implies E = \frac{1}{\sqrt{2} } + \frac{1}{\sqrt{2} }$

$:\implies E = \frac{2}{\sqrt{2} }$

$:\implies E = \sqrt{2} = 1.414$

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$\boxed{\boxed{\bold{\therefore Maximun\;value\;of\; Expression \;E = \sqrt{2} }}}$

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Hope this helps u.../

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