prove that cosec²A/cosecA-1-cosecA/cosecA+1=2sec²A
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Answered by
9
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
************************
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.
: )
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
************************
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.
: )
Answered by
5
Hi,
Please see the attached file!
Thanks
Please see the attached file!
Thanks
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