How do you prove #tan(1/2theta)=csctheta-cottheta#?

Related questions

• What does it mean to prove a trigonometric identity?
• How do you prove #\csc \theta \times \tan \theta = \sec \theta#?
• How do you prove #(1-\cos^2 x)(1+\cot^2 x) = 1#?
• How do you show that #2 \sin x \cos x = \sin 2x#? is true for #(5pi)/6#?
• How do you prove that #sec xcot x = csc x#?
• How do you prove that #cos 2x(1 + tan 2x) = 1#?
• How do you prove that #(2sinx)/[secx(cos4x-sin4x)]=tan2x#?
• How do you verify the identity: #-cotx =(sin3x+sinx)/(cos3x-cosx)#?
• How do you prove that #(tanx+cosx)/(1+sinx)=secx#?
• How do you prove the identity #(sinx - cosx)/(sinx + cosx) = (2sin^2x-1)/(1+2sinxcosx)#?