Question

how to prove this identity?
cosec A-2cot2AcosA=2sinA

Answer 1

\[LHS: {1 \over \sin A} - 2{\cos2 A \over \sin 2A}cosA = {1 \over sinA} - {\cos2A * cosA \over 2cosAsinA}\]

\[{1 \over sinA} - {\cos2A \over sinA} = {1-\cos2A \over sinA}\]

since cos2A = 1-sin^2 A:

\[{1 - (1-2\sin^2 A)\over sinA} = {2\sin^2 A \over \sin A } = 2\sin A\]

LHS = RHS