" Prove the following : "(4)/(pi)

Prove the following : cos^4(pi/8)+cos^4((3pi)/8)+cos^4((5pi)/8)+cos^4((7pi)/8) =3/2

Prove the following: (tan(pi/4+x))/(tan(pi/4-x))=((1+tanx)/(1-tanx))^2

Prove the following: cos((3pi)/4+x)-cos((3pi)/4-x)=-sqrt2 sinx

Prove the following: tan[(pi)/(4)+(1)/(2)cos^(-1)((a)/(b))]+tan[(pi)/(4)-(1)/(2)cos^(-1)((a)/(b))]=(2b)/(a)

Prove the following cos ((pi) / (4) -x) cos ((pi) / (4) -y) -sin ((pi) / (4) -x) sin ((pi) / (4) - y) = sin (x + y)

Prove the following int_(0)^((pi)/(4))2tan^(3)xdx=1-log2

Prove the following: 4cosxcos(pi/3+x)cos(pi/3-x)=cos3x

Prove the following: cos(pi/4+x)+cos(pi/4-x)=sqrt2cosx

Prove the followings : tan(pi/4+1/2"cos"^(-1)a/b)+tan(pi/4-1/2"cos"^(-1)a/b)=(2b)/a

Prove the following overset((pi)/(4)) underset(0) int 2 tan^(3)x dx=1- log 2