Question

show that (3 sin A - cos 2A-1) / (sin² A+2 sin A) = 2 - cosec A

Answer 1

rearrange the right side to look more attainable

\[\frac{ 3sinA-\cos2A-1 }{ \sin^{2}A+2sinA }=2-\frac{ 1 }{ sinA }\]

redoing the right again; left: remember your double angles to make cos2A = 1-sin^2A

\[\frac{2sin^2A+ 3sinA-2 }{ \sin^{2}A+2sinA }=\frac{ 2sinA-1 }{ sinA }\]

factor top and bottom and simplify