If then at is :

Engineering

Mathematics

Derivative of Standard Functions

Trigonometric Ratio of Multiple and Submultiples Angles

Question

If $y (α) \sqrt{2 (\frac{tanα + cotα}{1 + \tan^{2} α}) + \frac{1}{\sin^{2} α}}, α \in (\frac{3 π}{4}, π)$ then $\frac{dy}{dα}$ at $α = \frac{5 π}{6}$ is :

– 4

$- \frac{1}{4}$

$\frac{4}{3}$

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$y = \sqrt{\frac{2 \cos^{2} α}{sinαcosα} + \frac{1}{\sin^{2} α}} = \sqrt{2 cotα + {cosec}^{2} α} = | 1 + cotα | = - 1 - cotα$

$\frac{dy}{dα} = {cosec}^{2} α \Rightarrow (\frac{dy}{dα}) at α = \frac{5 π}{6}$ will be = 4