Question

Y=sinx cosx
$y = sin(x) cos(x)$
​

Answer 1

Step-by-step explanation:

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Secondary School Math 5 points

Y= cosx+sinx/cosx - sinx , show that dy/dx= sec square (pi/4 +x) . explain

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Answers

kumarsriram19p62r7g

kumarsriram19p62r7g Ambitious

Its simple and hence proved

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9 votes

THANKS

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harendrachoubay Expert

\dfrac{dy}{dx} =\sec^2 (\dfrac{\pi}{4}+x), proved.

Step-by-step explanation:

y=\dfrac{\cos x+\sin x}{\cos x-\sin x}

To prove that, \dfrac{dy}{dx} =\sec^2 (\dfrac{\pi}{4}+x)

∴ y=\dfrac{\cos x+\sin x}{\cos x-\sin x}

⇒y=\dfrac{\dfrac{\cos x+\sin x}{\cos x}}{\dfrac{\cos x-\sin x}{\cos x}}

Dividing nemerator and denominator by \cos x, we get

⇒ y=\dfrac{1+\tan x}{1-\tan x}

⇒y=\dfrac{\tan \dfrac{\pi}{4} +\tan x}{1-\tan \dfrac{\pi}{4}\tan x}

[ ∵ \tan (A +B})=\dfrac{\tan A +\tan B}{1-\tan A\tan B}]

⇒ y=\tan (\dfrac{\pi}{4} +x})

Differentiating both sides w.r.t. x, we get

\dfrac{dy}{dx} =\sec^2 (\dfrac{\pi}{4}+x), proved.

Answer 2

Answer:

cosx..sinx...2378916..