" (iii) "(1)/(sqrt(2))cos((pi)/(4)+x)=(1)/(2)(cos x-sin x)

Prove that cos((pi)/(4)-x)cos((pi)/(4)+x)=(1)/(2)-sin^(2)x

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

If I=int(sin x+sin^(3)x)/(cos2x)dx=P cos x+Q log|f(x)|+R then (a)P=(1)/(2),Q=-(3)/(4sqrt(2))(b)P=(1)/(4),Q=(1)/(sqrt(2)) (c) f(x)=(sqrt(2)cos x+1)/(sqrt(2)cos x-1)(d)f(x)=(sqrt(2)cos x-1)/(sqrt(2)cos x+1)

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

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

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

Prove that cos^(-1)((sqrt(1+x)+sqrt(1-x))/(2))=(pi)/(4)-(1)/(2)cos^(-1)x

Prove that cos ((3pi)/(4)+x)-cos ((3pi)/(4)-x)=-sqrt2 sin x

Prove that tan^(-1)((sqrt(1+x)-sqrt(1-sin x))/(sqrt(1+x)-sqrt(1-sin x)))=(pi)/(4)-(1)/(2)cos^(-1),-(1)/(sqrt(2))<=x<=1

lim_(xto(pi)) (1-sin(x/2))/(cos(x/2)(cos(x/4)-sin(x/4)))