Question

cot^2 (u/2) = (csc(u) + cot u)/(csc(u) - cot u)

Answer 1

RS = (1/sinu + cosu/sinu) / (1/sinu - cosu/sinu)

= [ (1+cosu)/sinu ] / [ (1 - cosu)/sinu ]
= (1+cosu)/sinu * sinu/(1-cosu)
= (1+ cosu)/(1 - cosu)

for the RS, use fact that cos^2 (A/2) = (cosA + 1)/2
and sin^2 (A/2) = (1 - cosA)/2

RS = cot^2 (u/2)
= cos^2 (u/2) / sin^2 (u/2)
= ((cosu + 1)/2) / ((1 - cosu)/2)
= (1 + cosu) / (1 - cosu)
= LS