Question

prove that cotA-cot2A=cosec2A

Answer 1

COTA-COT2A=COSEC2A
COSA/SINA -COS2A/SIN2A=1/SIN2A
SIN2ACOSA/COSA -COS2ASINA/SINA=1
SIN2ACOSA-COS2ASINA=SINA
SIN(2A-A)=SINA
SINA=SINA

Hope my answer helps u....

Answer 2

Prove that,
cotA-cot2A = cosec2A
LHS = cotA-cot2A
        = cosA/sinA - cos2A/sin2A
        = (cosA.sin2A - cos2A.sinA)/sinA.sin2A
        = (sin2A.cosA-cos2A.sinA)/sinA.sin2A
        = sin(2A-A)/sinA.sin2A
        = sinA/sinA.sin2A
        = 1/sin2A
        = cosec2A 
L.H.S = R.H.S