Question

sinA/cotA+cosecA=2+(sineA/cotA-cosecA)

Answer 1

LHS = 
sinA/(cotA+cosecA)
= (sinA)(cosecA-cotA)/(cosecA+cotA)(cosecA-cotA)
= (1-cosA)/(cosec2A-cot2A)
= (1-cosA)/1 = 1-cosA

RHS = 
2+(sinA)/(cotA-cosecA)
= 2+(sinA)(cotA+cosecA)/(cotA-cosecA)(cotA+cosecA)
= 2+(cosA+1)/(cot2A-cosec2A)
= 2+(cosA+1)/(-1)
= 2-cosA-1
= 1-cosA

LHS=RHS=1-cosA
Hence proved

Answer 2

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