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

Prove that: cos(pi/4-A)cos(pi/4-B)-sin(pi/4-A)sin(pi/4-B)="sin"(A+B)

Find the value of cos""(pi)/(12)(sin""(5pi)/(12)+cos""(pi)/(4))+sin""(pi)/(12)(cos""(5pi)/(12)-sin""(pi)/(4)) .

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

("cos"^(4)(pi)/(24)-"sin"^(4)(pi)/(24)) equals :

If A+B+C=pi , prove that : (sin ((B+C)/(2)) + sin ((C+A)/(2)) + sin( (A+B)/(2) )) equals (4cos ((pi-A)/(4)) cos( (pi-B)/(4)) cos((pi-C)/(4))) .

Evaluate the following: cos(2pi/3)cos(pi/4)-sin(2pi/3)sin(pi/4)

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

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

int_(-pi//4)^(pi//4) e^(-x)sin x" dx" is

If y="sec"(tan^(-1)x),t h e n (dy)/(dx) at x=1 is (a) cos(pi/4) (b) sin(pi/2) (c) sin(pi/6) (d) cos(pi/3)