calculus · worked example

Solve tan(x) = sec^2(x)

Method: sin/cos पर भागफल नियम. Verified step-by-step solution with our free AI math solver.
Problem

ddxtan(x)\frac{d}{dx}\tan(x)

Step-by-step solution

  1. tanx=sinxcosx\tan x = \frac{\sin x}{\cos x} के रूप में फिर से लिखें।

  2. भागफल नियम लागू करें: (fg)=fgfgg2\left(\frac{f}{g}\right)' = \frac{f'g - fg'}{g^2}

  3. f=sinxf = \sin x (f=cosxf' = \cos x) और g=cosxg = \cos x (g=sinxg' = -\sin x) के साथ: cosxcosxsinx(sinx)cos2x=cos2x+sin2xcos2x\frac{\cos x \cdot \cos x - \sin x \cdot (-\sin x)}{\cos^2 x} = \frac{\cos^2 x + \sin^2 x}{\cos^2 x}

  4. पाइथागोरस सर्वसमिका sin2+cos2=1\sin^2 + \cos^2 = 1 का उपयोग करें: =1cos2x=sec2x= \frac{1}{\cos^2 x} = \sec^2 x

Answer

sec2(x)\sec^2(x)

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