Question

$dfrac{sin x+1}{cos x}= hbox{tg} left( dfrac{x}{2}+dfrac{pi}{4}right)$

Answer 1

(sinx/2+cosx/2)^2/(cos^2x/2-sin^2x/2)=(sinx/2+cosx/2)/(cosx/2-sinx/2)=

=(tgx/2+1)/(1-tgx/2)=(tgП/4+tgx/2)/(1-tgП/4*tgx/2)=tg(x/2+П/4)