Among the following equations which is consistent in `(0, pi/2)` (a) `sinx+x^2 =0`

Find the principal solutions of each of the following equations : (i) sinx=(-1)/(2) "sin "(3x)/(2)=0 (iii) sin(x+(pi)/(5))=0 (iv) cos2x=0 (v) "cos"(5x)/(2)=0 (vi) cos(x+(pi)/(10))=0

Find the number of solution(s) of following equations: (i) x^(2)-sinx-cosx+2=0 (ii) sin^(2)x - 2sinx - x^(2)-3=0, x in [0,2pi]

Find the number of solution(s) of the following questions (a) x^2 + x + 1 + sinx = 0, x in [0, 2pi] (b) x^2 + x + 1 + sinx = 0, x in [pi, 2pi] (c) x^2 + x + sinx = 0, x in [0, pi]

No. of solution in the equation x=4sinx when in [0,2pi]

Differentiate the following function with respect to x : sin^(-1)(sinx),x in [0,2pi] cos^(-1)(cosx),x in [0,2pi] tan^(-1)(tanx),x in [0,pi]-{pi/2}

Prove the following (i) f(x)=sinx is : (I) strictly increasing in (0, (pi)/(2)) (II) strictly decreasing in ((pi)/(2), pi) (III) neither increasing nor decreasing in (0, pi) (ii) f(x)=2sinx+1 is an increasing function on [0, (pi)/(2)].

Solve the following differential equations. dy/dx+ 2y tan x =sinx,y(pi/3)=0

Find the intervals in which the following functions are increasing or decreasing : sinx + cos x, 0 le x le 2 pi

Solve the following differential equations: (dy)/(dx)-(tanx)y=sinxe^(sinx) , 0

Number of integral values of a for which the equation cos^2x-sinx+a=0 has roots when x in (0,pi/2) is____________