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

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

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

(cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x

What is the value of cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)?

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

((sin (pi/8)+i cos (pi/8))/(sin (pi/8)-i cos (pi/8)))^(8)=

int_0^(4/pi) (3x^(2) sin (1/x) - x cos (1/x)dx =

int_0^(pi/4) (cos x- sin x) dx + int_(pi/4)^((5pi)/4) (sinx-cosx) dx + int_(2pi)^(pi/4) (cosx- sinx) dx =

int_0^(pi//4) (sin x + cos x)/(3 + sin 2x ) dx =