सिद्ध कीजिए कि : `cos.(2pi)/(3)cos.(pi)/(4)-sin.(2pi)/(3)sin.(pi)/(4)=(-(sqrt3+1))/(2sqrt2)`

Evaluate cos (2pi/3)cos (pi/4)-sin(2pi/3)sin(pi/4)

Prove that (i) "sin " (7pi)/(12) " cos " (pi)/(2) - "cos " *(7pi)/(12) " sin " (pi)/(4) = (sqrt(3))/(2) (ii) " sin " (pi)/(4) " cos " (pi)/(2) + "cos"(pi)/(4) " sin " (pi)/(12) = (sqrt(3))/(2) (iii) " cos " (2pi)/(3) " cos " (pi)/(4) - " sin " (2pi)/(3) " sin " (pi)/(4) =(-(sqrt(3) +1))/(2sqrt(2))

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

sin^(2)(pi)/(6)+cos^(2)(pi)/(3)-tan^(2)-(1)/(2)(pi)/(4)=-(1)/(2)

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

cos((3pi)/(4)+x)-cos ((3pi)/(4)-x)=-sqrt(2) sin x

" 1.Prove that : "sin^(2)(pi)/(6)+cos^(2)(pi)/(3)-tan^(2)(pi)/(4)=-(1)/(2)

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

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

sin^(2)""(2pi)/(3)+ cos^(2)""(5pi)/6-tan^(2)""(3pi)/4=