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Prove that 1/cosec-cot-1/sin =1/sin - 1/cosec + cot

Prove that 1/cosec-cot-1/sin =1/sin - 1/cosec + cot

Grade:10

3 Answers

Arun
25750 Points
6 years ago
Dear Keshav 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
Regards
Arun (askIITians forum expert)
Sankalp Das
25 Points
6 years ago
=(cosecx)^2-(cotx)^2=1...=cosecx-cotx=1/cosecx+cotxTherefore,1/cosecx-cotx-1/sinx ...=cosecx+cotx-cosecx=1/sinx-(cosecx-cotx)=1/sinx-1/cosecx+cotx...hp
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the attached solution to your problem.
 
LHS= 1/(cosecA – cotA) – 1/sinA
=(cosecA + cotA)/cosec2A – cot2A) – cosecA
=cosecA + cotA – cosecA
=cotA
RHS=1/sinA – 1/(cosecA + cotA)
=cosecA-(cosecA – cotA)/(cosec2A – cot2A)
=cosecA-(cosecA – cotA)
=cotA
LHS=RHS
Hence proved.
 
Hope it helps.
Thanks and regards,
Kushagra

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