Trigg proving question (FIRST ONE WHO GETS IT CORRECT GETS 10 POINTS)!!!!

Prove cot(A) + cosec(A) = cot(A/2)

show full solution

cot(A) + cosec(A) = cot(A/2)

LHS
= cot(A) + cosec(A)
= [cos(A)/sin(A)] + 1/sin(A)
= [cos(A) + 1] / sin(A)
= [1+2cos²(A/2) - 1] / [2sin(A/2)cos(A/2)]
= [2cos²(A/2)] / [2sin(A/2)cos(A/2)]
= cos(A/2) / sin(A/2)
= cot (A/2)
= RHS

That's about it!