Prove that :` cos (pi/12) - sin (pi/12) = 1/sqrt(2)`

Prove that: i) sin(5pi)/(18) - cos(4pi)/(9) = sqrt(3)sinpi/9 ii) cos(3pi)/4+A-cos((3pi)/(4)-A)=-sqrt(2)sinA

Prove that; 2(sin(5 pi))/(12)(sin pi)/(12)=(1)/(2)

Prove that (i) " 2sin " (5pi)/(12) " sin " (pi)/(12)=(1)/(2) (ii) " 2 cos " (5pi)/(12) " cos " .(pi)/(12)=(1)/(2) (iii) " 2 sin ".(5pi)/(12) " cos " (pi)/(2) = ((2+sqrt(3))/(2))

Prove that: sin^(2)(pi/8+A/2)-sin^(2)(pi/8-A/2)=1/sqrt(2)sinA

Prove that: cos(pi/4+A)+cos(pi/4-A)=sqrt(2)cosA

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))

Prove that 2sin((5 pi)/(12))cos((pi)/(12))=(2+sqrt(3))/(2)

Prove that tan ((pi) / (12)) * tan (5 (pi) / (12)) * tan (7 (pi) / (12)) * tan (11 (pi) / (12)) = 1

Prove that (i) " sin " .(pi)/(6). " cos " .(pi)/(6) = (sqrt(3))/(4) " " (iii) cos^(2) .(pi)/(2) - sin^(2) .(pi)/(2) =(sqrt(3))/(2)

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