Question

prove that cosec²A/cosecA-1-cosecA/cosecA+1=2sec²A

Answer 1

Hi ,

LHS = cosec²A/(cosecA-1) -cosec²A/(Cosec A+1)

=cosec²A[(cosecA+1)-(cosecA-1)]/[(cosecA+1)(cosecA-1)]

=cosec²A [(cosecA+1-cosecA+1)/(cosec² A-1)]

= ( 2cosec²A)/cot² A

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We know the trigonometric identity

1 ) cosec² A - 1 = cot² A

2 ) cosecA = 1/sinA

3 ) cotA = cosA/sinA

******************************†

= ( 2/sin²A )/( cos² A/sin² A )

= 2/cos² A

= 2sec²A

= RHS

I hope this helps you.

: )

Answer 2

Hi,

Please see the attached file!


Thanks