Cosa/cosec a+1 +cosa/cosec a-1=2tan a
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LHS
[cosA/(cosecA+1)] + [cosA/(cosec-1)]
Taking LCM
=[cosA(cosec-1) + cosA(cosecA+1)]/[(cosecA+1)(cosecA-1)
cosAcosecA = cosA /sinA = cotA
and, (cosecA+1)(cosecA-1)= cosec²A -1 = cot²A
now, substituting these values,
(cotA -cosA)+(cotA +cosA)/cot²A
=2cotA/cot²A
=2/cotA
=2tanA
RHS
[cosA/(cosecA+1)] + [cosA/(cosec-1)]
Taking LCM
=[cosA(cosec-1) + cosA(cosecA+1)]/[(cosecA+1)(cosecA-1)
cosAcosecA = cosA /sinA = cotA
and, (cosecA+1)(cosecA-1)= cosec²A -1 = cot²A
now, substituting these values,
(cotA -cosA)+(cotA +cosA)/cot²A
=2cotA/cot²A
=2/cotA
=2tanA
RHS
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