If ` A B C` having vertices `A(acostheta_1,asintheta_1),B(acostheta_2asintheta_2),a n dC(acostheta_3,asintheta_3)` is equilateral, then prove that `costheta_1+costheta_2+costheta_3=sintheta_1+sintheta_2+sintheta_3=0.`

Prove that (1-costheta +cos2theta )/(sin2theta -sintheta)=cottheta

If (acostheta_1,asintheta_1),(acostheta_2,asintheta_2) and (acostheta_3,asintheta_3) represent the vertices of an equilateral triangle inscribed in a circle, then (a) costheta_1+costheta_2+costheta_3=0 (b) sintheta_1+sintheta_2+sintheta_3=0 (c) tantheta_1+tantheta_2+tantheta_3=0 (d) cottheta_1+cottheta_2+cottheta_3=0

Prove that (sintheta)/(cosectheta+cottheta)=1-costheta

costheta -sintheta -cottheta +1=0

Prove that (cottheta+cosectheta-1)/(cottheta-cosectheta+1)=(1+costheta)/sintheta

Prove that (sintheta +sin2theta)/(1+costheta +cos2theta)=tantheta

Prove that: (1+sintheta-costheta)/(1+sintheta+costheta)=tantheta/2

Prove that (tantheta +sectheta -1)/(tantheta-sectheta+1)=(1+sintheta)/costheta

(sintheta+sin2theta)/(1+costheta+cos2theta)