If y α = 2 t a n α + c o t α 1 + t a n 2 α + 1 s i n 2 α , α ∈ 3 π 4 , π , then d y d α at α = 5 π 6 is

Simplifying using Trigonometric Identity, we get, y α = 1 + cot α or, y α = - 1 + cot α , as α ∈ 3 π 4 , π Hence, d y d α = cos e c 2 α ∴ d y d α α = 5 π 6 = 4

Mathematics - Differentiation Question with Solution | TestHub

MathematicsDifferentiationDifferentiation of composite functionsMedium2 minPYQ_2020

MathematicsMediumsingle choice

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

Options:

Answer:

Solution:

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, $\frac{d y}{d α} = \cos e c^{2} α$

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

Stream:JEESubject:MathematicsTopic:DifferentiationSubtopic:Differentiation of composite functions

⏱ 2mℹ️ Source: PYQ_2020

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