For all x in `0 le x le (pi)/(2)`, show that,
cos(sin x) > sin(cos x)

If 0 le x le (pi)/(2) and 81^(sin ^(2)x)+81^(cos^(2) x)=30, then the value of x is -

Find the area bounded by the following curve : (i) f(x) = sinx, g(x) = sin^(2)x, 0 le x le 2pi (ii) f(x) = sinx, g(x) = sin^(4)x, 0 le x le 2pi

If x in (0,pi/2), then show that cos^(-1)(7/2(1+cos2x)+sqrt((sin^2x-48cos^2x))sinx)=x-cos^(-1)(7cosx)

Show that for all real value of x, c-sqrt(a^(2) + b^(2)) le a cos x + b sin x + c le c + sqrt(a^(2) + b^(2))

Let f(x) = {{:(x^(2) + 3x",", -1 le x lt 0),(-sin x",", 0 le x lt pi//2),(-1 - cos x",", (pi)/(2) le x le pi):} . Draw the graph of the function and find the following (a) Range of the function (b) Point of inflection (c) Point of local minima

2 sin^2(pi/2 cos^2 x) = 1 - cos(pi sin 2x) . if

Show that 3(sin^4x+cos^4x)-2(sin^6x+cos^6x)=1 .

int _(0)^((pi)/(4)) (sin x+cos x)/(9+16 sin 2x)dx

cos^(2) x dy/dx + y = tanx [0le x le pi/2]

If (cos^4x)/(cos^2y)+(sin^4x)/(sin^2y)=1,"show taht", (cos^4y)/(cos^2x)+(sin^4y)/(sin^2x)=1