Plot `y=sin(x+(pi)/(4)) and y =sin(x-(pi)/(4))`.

cos ((pi)/(4) - x) cos ((pi)/(4) -y) - sin ((pi)/(4) -x) sin ((pi)/(4) -y) = sin ( x +y)

The rangeof the function y=f(x)=sin[x] , (-pi)/(4)lt x lt (pi)/(4) , where [x] denotes the greatest integer le x, is :

sin^(-1)("sin"(pi)/4)

If tan (pi cos theta)=cot (pi sin theta), 0ltthetalt(3 pi)/(4) then, sin (theta+(pi)/(4)) equals

The value of sqrt(2)int(sinx)/(sin(x-(pi)/(4)))dx is :

cos ((3pi)/( 4) + x) - cos((3pi)/( 4) -x) =- sqrt2 sin x

Prove geometrically that cos(x + y) = cos x cos y - sinx sin y and hence prove cos((pi)/(2) + x) = - sin x .

The area of the region bound by Y-axis, y = cos x and y = sin x, 0lexle (pi)/(2) is