cos x=-(1)/(sqrt(2))

The relation int(sin2x+cos2x)=(1)/(sqrt(2))sin(2x-a)+c is true for

The relation int(sin2x+cos2x)=(1)/(sqrt(2))sin(2x-a)+c is true for

int(2sin x)/((3+sin2x))dx is equal to (1)/(2)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+c(1)/(2)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(2sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+c(1)/(4)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+cnone of these

General solution of cos3x=(1)/(sqrt(2)) is

int_(0)^((pi)/(2))(cos^(2)x)/(sin x+cos x)dx=(1)/(sqrt(2))(log(sqrt(2)+1))

Prove that: tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x+sqrt(1-x)))]=(pi)/(4)-(1)/(2)cos^(-1)x,quad -(1)/(sqrt(2))<=x<=1

Prove that cos[tan^(-1){sin(cos^(-1)x)}]=(1)/(sqrt(2-x^(2)))

Prove that sin^(-1)(2x.sqrt(1-x^(2)))=2cos^(-1)x,(1)/(sqrt(2))lexlt1