Question

Prove that tanA ÷secA-1+tana÷secA+1=2cosecA

Answer 1

please let me know if you need anything else

Answer 2

LHS =tanA/ secA-1+tanA/secA+1
=sinA/cosA/1/cosA-1+sinA/cosA/1/cosA+1[bcoz tanA=sinA/cosA and secA=1/cosA]
=sinA/cosA/(1-cosA) / cosA +sinA/cosA/(1+cosA)/cosA
=sinA/1-cosA+sinA/1+cosA
=[sinA(1+cosA)+sinA(1-cosA) ] /(1-cosA) (1+cosA)
=[sinA+sinA.cosA+sinA-sinA. cosA] / 1-cos(sq)A
=2sinA/sin(sq)A [from identity : sin(sq)A+cos(sq)A=1]

=2/sinA
=2 * 1/sinA
=2cosecA
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