PROVE: sinA/cotA+cosecA=2+ sinA/cotA-cosecA
Asked by Krithi K
6th April 2012,
9:14 PM
Answered by Expert
Answer:
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
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
Answered by Expert
8th April 2012,
4:04 PM
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