[" (iii) "sin20^(@)+sin140^(@)+cos170^(@)=0],[(iv)cos(pi)/(12)-sin(pi)/(12)=(1)/(sqrt(2))]

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

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

2sin((5 pi)/(12))(sin((pi)/(12)))=

(cos(pi/12)-sin(pi/12))(tan(pi/12)+cot(pi/12))=

"sin" pi/12 "sin" (5pi)/12=

(sin((5pi)/12)-cos((5pi)/12))/(cos((5pi)/12)+sin((5pi)/12))=

Prove that, (sin""(5pi)/(12)-cos""(5pi)/(12))/(cos""(5pi)/(12)+sin""(5pi)/(12))=(1)/(sqrt(3))

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))