[=cos x-cos x+],[=R*H.S],[" ii) "L.H.S.=cos((3 pi)/(2)+x)]

(cos (pi + x) cos (-x)) / (sin (pi-x) cos ((pi) / (2) -x)) = cot ^ (2) x

Prove that (i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x) (ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x (iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) " (iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0

(cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x

(cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x

(cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x

(cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x

(cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x

Prove that (i) " cos " ((pi)/(4) + x) + " cos " ((pi)/(4)- x) =sqrt(2) " cos " x (ii) " cos " ((3pi)/(4) + x) - "cos " ((3pi)/(4)-x) =- sqrt(2) " sin " x

Prove that (i) " cos " ((pi)/(4) + x) + " cos " ((pi)/(4)- x) =sqrt(2) " cos " x (ii) " cos " ((3pi)/(4) + x) - "cos " ((3pi)/(4)-x) =- sqrt(2) " sin " x

Find the extreme values of the following function over R. (i) sin^(2) (60^(0) + x) + sin^(2) (60^(0) - x) (ii) cos (x+ (Pi)/(3) ) + 2sqrt(2) sin (x+ (pi)/(3))-3 (iii) 3 sin^(2) x+ 5 cos^(2) x (iv) cos 2 x+ cos^(2) x (v ) cos x cos ((2pi)/(3) + x) cos ((2pi)/(3)-x)