Given that, `tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha)`
`rArr" "tantheta=(cosalpha(tanalpha-1))/(cosalpha(tanalpha+1))`
`rArr" "tantheta=(tanalpha-tan""(pi)/(4))/(1+tan""(pi)/(4)*tanalpha)" "[becausetan ""(pi)/(4)=1]`
`rArr" " tantheta=tan (alpha-(pi)/(4))`
` rArr" "theta=alpha-(pi)/(4)rArralpha=theta+(pi)/(4) ` ltBrgt `therefore" "sinalpha+cosalpha=sin(theta+(pi)/(4))+cos(theta+(pi)/(4))`
`" "=sin theta*cos""(pi)/(4)+costheta*sin""(pi)/(4) +costheta *cos""(pi)/(4)-sintheta*sin""(pi )/(4)`
`" "= (1)/(sqrt (2))sintheta+(1)/(sqrt(2))costheta+(1)/(sqrt(2))costheta-(1)/(sqrt(2)sintheta)[becausesin""(pi)/(4)=cos""(pi)/(4)=(1)/(sqrt(2))]`
`" "=(2)/(sqrt(2))*costheta=sqrt(2)costheta`
