Question

prove tanA /secA-1 + tanA/ secA +1 = 2cosecA

Answer 1

Taking L. H. S.
=tanA/secA-1+tanA/sec+1
TAKING L. C. M.
=tanA(secA+1+secA-1/sec²-1)
=tanA(2secA/tan²A)
=2secA/tanA
=2 x 1/cosA x cosA/sinA
=2/sinA
=2cosecA

Answer 2

Hey !!!

from LHS

tanA /secA -1 + tanA/secA+1

tanA (secA+1) + tanA(secA-1)
---------------------------------------
(sec²-1) lcm

tanA×secA + tanA + tanA×secA - tanA
-----------------------------------------------------
tan²A

sinA/cosA×1/cosA + sinA/cosA×1/cosA
-----------------------------------------------------
tan²A

sinA/cos²A + sinA/cos²A
----------------------------------
sin²A/cos²A

2sinA/cos²A
-----------------
sin²A/cos²A

2/sinA

cosecA [ RHS prooved ]


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Hope it helps you !!!

@Rajukumar111