If `y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3` is `(1-sqrt(3))/2` (b) 0 (c) `1/2(sqrt(3)-1)` (d) none of these

If y=|cosx|+|sinx| , then (dy)/(dx)" at "x=(2pi)/(3) is

If y=cos^(-1)(cosx),t h e n(dy)/(dx) at x=(5pi)/4 is equal to (a)1 (b)-1 (c)0 (d)4

The solution for x of the equation int_(sqrt(2))^(x)(dt)/(sqrt(t^(2)-1))=(pi)/(2) is pi(b)(sqrt(3))/(2) (c) 2sqrt(2) (d) none of these

If x=cos t and y=sin t, prove that (dy)/(dx)=(1)/(sqrt(3)) at t=(2 pi)/(3)

int_-(pi/3)^(pi/3) (x^3cosx)/sin^2xdx= (A) 0 (B) 1 (C) -1 (D) none of these

If tan^(-1)(a+x)/a+tan^(-1)(a-x)/a=pi/6,t h e nx^2= 2sqrt(3)a (b) sqrt(3)a (c) 2sqrt(3)a^2 (d) none of these

e^(x)=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t)) andtan (y)/(2)=sqrt((1-t)/(1+t)) then (dy)/(dx) at t=(1)/(2) is (a)-(1)/(2) (b) (1)/(2)(c)0(d) none of these

Given b=2,c=sqrt(3),/_A=30^(0), then inradius of o+ABC is (sqrt(3)-1)/(2) (b) (sqrt(3)+1)/(2) (c) (sqrt(3)-1)/(4) (d) none of these

In ABC, the coordinates of B are (0,0),AB=2,/_ABC=(pi)/(3), and the middle point of BC has coordinates (2,0) .The centroid o the triangle is ((1)/(2),(sqrt(3))/(2))(b)((5)/(3),(1)/(sqrt(3)))(4+(sqrt(3))/(3),(1)/(3))( d) none of these

If x=3tan t and y=3sec t then find (d^(2)y)/(dx^(2)) at x=(pi)/(4)( a) 3( b) (1)/(6sqrt(2))(c)1(d)(1)/(6)