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

Find the area of the region bounded by the curve y= sin x, x = (pi)/(2) and x =(3 pi)/(2) .

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

Prove that, sin^(2)((pi)/(18))+sin^(2)((pi)/(9))+sin^(2)((7pi)/(18))+sin^(2)((4pi)/(9))=2

The phase difference between two SHM y_(1) = 10 sin (10 pi t + (pi)/(3)) and y_(2) = 12 sin (8 pi t + (pi)/(4)) to t = 0.5s is

Obtain the particular solution of the differential equation: { x cos ((y)/( x)) + y sin ((y)/( x))} ydx= { y sin ((y)/( x) ) - x cos ((y)/( x))}xdy where : x=2 when y= (pi)/(2) .

f(x)= sin^(2)x + sin^(2) (x + (pi)/(3)) + cos x cos (x + (pi)/(3)) and g(5 / 4)' =1 then (gof)(x) = ………

The number of solution for , {:(sin(x-(pi)/4)-cos(x+(3pi)/4)=1),(" "(2cos 7x)/(cos 3+sin3) gt 2^(cos 2x)):}}" in" (0,2pi) is

overset((pi)/(4))underset(-(pi)/(4))int log (sin x+cosx)dx

Prove that, 3sin((pi)/(6))sec((pi)/(3))-4sin((5pi)/(6))cot((pi)/(4))=1 .

Evaluation of definite integrals by subsitiution and properties of its : int_(theta)^(pi/2)|sin(x-(pi)/(4))|dx=.........