Prove that `cosx/(2+cosx)=1-2/(2+cosx)`

Prove that (1+sinx-cosx)/(1+sinx+cosx) +(1+sinx+cosx)/(1+sinx-cosx) =2 cosec x

Prove that (1+sinx-cosx)/(1+sinx+cosx) +(1+sinx+cosx)/(1+sinx-cosx) =2 cosec x

intdx/((2+cosx)(3-cosx))

int(cosx)/(1-cosx)dx=

int(cosx)/(1+cosx)dx=

int (cosx-cos2x)/(1-cosx) dx

"If "y=(x)^(cosx)+(sinx)^(tanx)", prove that "(dy)/(dx)=x^(cosx){(cosx)/(x)-(sinx)logx}+(sinx)^(tanx).{1+(log sinx)sec^(2)x}.

int(1-cosx)/(cosx(1+cosx))dx

int(1-cosx)/(cosx(1+cosx))dx

int(sinx+2cosx)/(2sinx+cosx)dx