If `y^(2)+ln cos^(2)x=y, x in((-pi)/(2),(pi)/(2))` then

If y^(2)+log_(e)(cos^(2)x)=yx in (-(pi)/(2),(pi)/(2)) , then

If y^2+ln(cos^2x)=y , then

The area of the region bounded by the curve y=cos^(-1)(cos x),x in(-(pi)/(2),(pi)/(2)) and the straight lines x=-1 , x=1,y=(pi)/(2), is k then

If int_(0)^(pi//2) log cos x dx =(pi)/(2)log ((1)/(2)), then int_(0)^(pi//2) log sec x dx =

Suppose cos^(2)y.(dy)/(dx)=sin(x+y)+sin(x-y), |x| le (pi)/(2) and |y|le(pi)/(2). If y((pi)/(3))=-(pi)/(2), then y((pi)/(2)) is

If (dy)/(dx) + (4)/(cos^2 x) y = (1)/(cos^2 x) , x in ((-pi)/(3) , pi/3) " and " y (pi/6) = 4/3 " then " y (- pi/6) equals ,

Area bounded by y=tan x,y=tan^(2)x in between x in(-(pi)/(3),(pi)/(3)) is equal to ((pi)/(4)+ln sqrt(2)-1)

The number of points of intersection of 2y=1 and y=cos x in -(pi)/(2)<=x<(pi)/(2) is

The co-ordinates of points of intersection of the curves y=cos x and y=sin3x,x in[-(pi)/(2),(pi)/(2)] are

Consider a function,f(x)=(2)/(3)ln(sin x+cos x)^((3)/(2)) for x in(0,(pi)/(2)) The value of lim_(x rarr(pi)/(2))(f(x))/((pi)/(2)-x) is