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If y = log tan (π/4+X/2) …

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If y = log tan (π/4+X/2) show that dy/dx -sec X=0
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Aisha Gupta 7 years, 2 months ago

Y=log(1+tanx/2)/1-tanx/2 =>y=log[(cosx/2+sinx/2)/(cosx/2-sinx/2)]. =>y=log[(cosx/2+sinx/2)²/(cos²x/2-sin²x/2)] =>y=log(1+sinx)/cosx =>y=log(secx+tanx). Now diff w.r.t x dy/dx=secxtanx+sec²x/secx+tanx =>dy/dx=secx. =>dy/dx-secx=0
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