`sin(pi/4+A).sin(pi/4-A)=1/2 cos2A`

cos(pi/4-A)cos(pi/4-B)-sin(pi/4-A)sin(pi/4-B)=sin(A+B)

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

Let Q = [{: (cos ""(pi)/(4) , - sin""(pi)/(4)),(sin""(pi)/(4), cos""(pi)/(4)):}] and x = [{:((2)/(sqrt(2))),((1)/(sqrt(2))):}] then Q^(3) x is equal to

cos((pi)/(4)+A) cos((pi)/(4) - B) + sin ((pi)/(4) +A) * sin((pi)/4-B)=

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

Prove that : cos (pi/4- theta)cos (pi/4-phi)-sin(pi/4-theta) sin (pi/4-phi)= sin (theta+phi) .

sin (pi/2) = 2 sin(pi/4) cos (pi/4)

If A+B+C=180^(@) then prove that sin"A/2+"sin"B/2+"sin"C/2 =1+4sin((pi-A)/4)sin((pi-B)/4)cos((pi-C)/4)

Let P=(("cos"(pi)/(4),-"sin"(pi)/(4)),("sin"(pi)/(4),"cos"(pi)/(4))) and X=(((1)/(sqrt(2))),((1)/(sqrt(2)))) . Then P^(3)X is equal to

Prove that cos^2(pi/4-B)-sin^2(pi/4-A)=sin(A+B)cos(A-B)