PROOVE THAT 1/COSEC A - COT A - 1/SINA = 1/SIN A - 1/COSECA+COTA
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Step-by-step explanation:
1/(cosecA-cotA) -1/sinA
=(Cosec^2A-cot^2A)/(cosecA-cotA)-cosecA . (As cosec^2A-cot^2A=1)
=(CosecA+cotA)-cosecA
=CosecA-(CosecA-cotA)
=1/sinA-(cosecA-cotA)(cosecA+cotA)/(cosecA+cotA)
=1/sinA-(cosec^2A-cot^2A)/(cosecA+cotA)
=1/sinA-1/(cosecA+cotA)=RHS. Proved
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Answer:
Step-by-step explanation:
LHS=1/(cosecA-cotA) -1/sinA
=(cosecA+cotA)/cosec^2A-cot^2A) -cosecA
=cosecA+cotA-cosecA
=cotA
RHS=1/sinA-1/(cosecA+cotA)
=cosecA-(cosecA-cotA)/(cosec^2A-cot^2A)
=cosecA-(cosecA-cotA)
=cotA
LHS=RHS
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