If yα=√(2tanα+cotα1+tan^2α+1sin^2α), α∈(3π)/4,π, then dy/(dα) at α=(5π)/6 is

Q26 / 75 · JEE Main 2020 (07 Jan Shift 1) · Mathematics

If $y (α) = \sqrt{2 (\frac{t a n α + c o t α}{1 + t a n^{2} α}) + \frac{1}{s i n^{2} α}}, α \in (\frac{3 π}{4}, π)$ , then $\frac{d y}{d α}$ at $α = \frac{5 π}{6}$ is

Simplifying using Trigonometric Identity, we get,

$y (α) = |1 + \cot (α)|$

or, $y (α) = - (1 + \cot (α))$ , as $α \in (\frac{3 π}{4}, π)$

Hence, $\frac{d y}{d α} = \cos e c^{2} α$

${∴ \frac{d y}{d α}}_{α = \frac{5 π}{6}} = 4$

Hence, the correct answer is option: 'A'.