Show that :

`Cos(pi/4 ) Sin(pi/4 ) - Sin^2(pi/6 ) = Cos^2( pi/3 )`

cos(pi/4-A)-sin(pi/4+A)=0

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

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

cos ^ (2) (pi / 4 + x) -sin ^ (2) (pi / 4-x)

Prove that: (a) 2sin^(2)(pi/2) + "cosec"^(2)((7pi)/2) cos^(2)(pi/3)=(3/2)^2 (b) 2sin^(2)((3pi)/4)+2cos^(2)(pi/4)+2sec^(2)(pi/3)=10

sin pi/3 = 2sin pi/6 cos pi/6

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

Prove that (a) sin^(2)(pi/6) + cos^(2)( pi/3) - tan^(2)(pi/4) = -1/2 (b) sin((8pi)/3) cos((23pi)/6) + cos((13pi)/3) sin((35pi)/6) = 1/2

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

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