`y = cos x + C : y' + sin x = 0`

The area bounded by the y-axis, y = cos x and y = sin x when 0 le x le pi/4 is

y - cos y = x : (y sin y + cos y + x)y' = y

The area bounded by the Y-axis , y= cos x and y= sin x when 0 le x le (pi)/(2) is

y = e^(x)(a cos x + b sin x)

lf cos x + cosy-cos z = 0 = sin x + sin y + sin z then cos((x-y)/2)=

Statement I The system of linear equations x+(sin alpha )y+(cos alpha )z=0 x+(cos alpha ) y+(sin alpha )z=0 -x+(sin alpha )y-(cos alpha )z=0 has a not trivial solution for only one value of alpha lying between 0 and pi . Statement II |{:(sin x, cos x , cos x),( cos x , sin x , cos x) , (cos x , cos x , sin x ):}|=0 has no solution in the interval -pi//4 lt x lt pi//4 .

The area of the region bounded by the curve y= cos x,y = sin x,Y -axis and 0 le x le (pi)/(4) is ……. Sq. units.

Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. Some which of these represent (i) a travelling wave, (ii) a stationary wave or (iii) none at all: (a) y = 2 cos (3 x) sin (10 t) (b) y = 2 sqrt(x - v t) (c ) y = 3 sin (5 x - 0.5 t) + 4 cos(5 x - 0.5 t) (d) y = cos x sin t + cos 2x sin 2t

Verify that the function y = a cos x + b sin x , where a,b in R is a solution of the differential equation (d^(2)y)/(dx^(2)) + y = 0

The area of the region enclosed between the curves y= sinx + cos x and y= | cos x - sin x|, x in [ 0, pi/2] is ……..Sq. units.