(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

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

If f(x)=(sqrt(cos((pi)/(2)-x)))/(1-cos(x+(pi)/(2))^((1)/(3))) and g(x)=(1)/(sqrt([sin x])) then range of g(x)-f(x) contains

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 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

The number of solution for , {:(sin(x-(pi)/4)-cos(x+(3pi)/4)=1),(" "(2cos 7x)/(cos 3+sin3) gt 2^(cos 2x)):}}" in" (0,2pi) is