If y(α) = √2((tanα+cotα/1+tan2α))+(1/sin2α), α ϵ ((3π/4),π), then (dy/dα ) at α = (5π/6) is :

Question

If y(α) = √2((tanα+cotα/1+tan2α))+(1/sin2α), α ϵ ((3π/4),π), then (dy/dα ) at α = (5π/6) is : (A) -(1/4) (B) (4/3) (C) 4 (D) -4

Tardigrade Admin · Accepted Answer

y(α) = √2((tanα+cotα/1+tan2α))+(1/sin2α), α ϵ ((3π/4),π) =(|sin α + cos α|/|sin α |) = (-(sin α +cos α )/sin α ) = - 1 -cos α y' (α) = cosec2α y'((5π/6)) = 4

Q. If $y (α) = 2 (\frac{t an α + co t α}{1 + t a n ^{2} α}) + \frac{1}{s i n ^{2} α}, α ϵ (\frac{3 π}{4}, π),$ then $\frac{d y}{d α}$ at $α = \frac{5 π}{6}$ is :

$- \frac{1}{4}$

$\frac{4}{3}$

4

-4

$y (α) = 2 (\frac{t an α + co t α}{1 + t a n ^{2} α}) + \frac{1}{s i n ^{2} α}, α ϵ (\frac{3 π}{4}, π)$
$= \frac{∣ s in α + cos α ∣}{∣ s in α ∣} = \frac{- ( s in α + cos α )}{s in α}$
$= - 1 - cos α$
$y^{'} (α) = cose c^{2} α$
$y^{'} (\frac{5 π}{6}) = 4$

Q. If y(α)=2(1+tan2αtanα+cotα​)+sin2α1​​,αϵ(43π​,π), then dαdy​ at α=65π​ is :

−41​

34​

4

-4

y(α)=2(1+tan2αtanα+cotα​)+sin2α1​​,αϵ(43π​,π) =∣sinα∣∣sinα+cosα∣​=sinα−(sinα+cosα)​ =−1−cosα y′(α)=cosec2α y′(65π​)=4

Q. If $y (α) = 2 (\frac{t an α + co t α}{1 + t a n ^{2} α}) + \frac{1}{s i n ^{2} α}, α ϵ (\frac{3 π}{4}, π),$ then $\frac{d y}{d α}$ at $α = \frac{5 π}{6}$ is :

$- \frac{1}{4}$

$\frac{4}{3}$

$y (α) = 2 (\frac{t an α + co t α}{1 + t a n ^{2} α}) + \frac{1}{s i n ^{2} α}, α ϵ (\frac{3 π}{4}, π)$
$= \frac{∣ s in α + cos α ∣}{∣ s in α ∣} = \frac{- ( s in α + cos α )}{s in α}$
$= - 1 - cos α$
$y^{'} (α) = cose c^{2} α$
$y^{'} (\frac{5 π}{6}) = 4$