If $ \frac{d y}{d x}=\cos (x+y), y\left(\frac{\pi}{2}\right)=0 $, then $ y(0)= $

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

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Application +4 | -1

\frac{d y}{d x}=\cos (x+y), y\left(\frac{\pi}{2}\right)=0

, then

y(0)=

View answer and explanation

Correct option: D

-2 \tan ^{-1}\left(\frac{\pi}{2}-1\right)

Option D (

-2 \tan ^{-1}(\frac{\pi}{2}-1)

) is correct because solving the differential equation with the given initial condition and then evaluating at x=0 gives this result.

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f(x)=|x|^{|\tan x|}

f^{\prime}\left(\frac{-\pi}{6}\right)

x

y

x>0

x y=1

x+y

f(x)=[x] \sin (\pi x)

[x]

x

x=k, k

f(x)

y = {\sec ^{ - 1}}\left[ {\mathrm{cosec}x} \right] + \mathrm{cose}{\mathrm{c}^{ - 1}}\left[ {\sec x} \right] + {\sin ^{ - 1}}[\cos x] + {\cos ^{ - 1}}[\sin x],

\frac{{dy}}{{dx}}

\frac{d}{d x} \sin ^{-1}\left(3 x-4 x^{3}\right)

z = y + f\left( v \right),

v = \left( {\frac{x}{y}} \right),

v\frac{{\partial z}}{{\partial x}} + \frac{{\partial z}}{{\partial y}}