Question

тригонометрия помогите упростить

Answer 1

$sqrt{ctg^2(frac{x}{2})-1}=sqrt{cos^2(frac{x}{2})/sin^2(frac{x}{2})-1}=\ =sqrt{(cos^2(frac{x}{2})-sin^2(frac{x}{2}))/sin^2(frac{x}{2})}=\ =sqrt{(cosx)/sin^2(frac{x}{2})}=frac{sqrt{cosx}}{|sin(frac{x}{2})|}$

Answer 2

$sqrt{ctg^2(x/2)-1}= sqrt{cos^2(x/2)/sin^2(x/2)-1}= \ sqrt{(cos^2(x/2)-sin^2(x/2))/sin^2(x/2)}= sqrt{cosx/sin^2(x/2)}$