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Grade 12Differential Calculus

find dy/dx when
y= log(sqrt(1 – cos x/ 1 + cos x)

Profile image of taniska
11 Years agoGrade 12
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1 Answer

Profile image of Jitender Singh
11 Years ago
Ans:
Hello Student,
Please find answer to your question below

y = log(\sqrt{\frac{1-cosx}{1+cosx}})
y = log(\sqrt{\frac{2sin^{2}\frac{x}{2}}{2cos^{2}\frac{x}{2}}})
y = log(\sqrt{tan^{2}\frac{x}{2}})
y = log(tan\frac{x}{2})
\frac{dy}{dx} = \frac{1}{tan\frac{x}{2}}.sec^{2}\frac{x}{2}.\frac{1}{2}
\frac{dy}{dx} = \frac{cos\frac{x}{2}}{sin\frac{x}{2}}.sec^{2}\frac{x}{2}.\frac{1}{2}
\frac{dy}{dx} = \frac{1}{sin\frac{x}{2}.cos\frac{x}{2}}.\frac{1}{2}
\frac{dy}{dx} = \frac{1}{sinx}

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