Question

tanA/secA-1+tanA/secA+1=2cosecA​

Answer 1

Answer:

LHS = tanA/secA - 1 + tanA/secA + 1

= sinA/cosA / 1/cosA - 1 + sinA/cosA / 1/cosA + 1 [because tan A = sin A / cos A and sec A = 1 / cos A]

= sinA/cosA / (1 - cosA) / cosA + sinA/cosA / (1 + cosA) / cos A

= sinA / 1 - cosA + sinA / 1 + cos A

= [sinA (1 + cosA) + sinA (1 - cosA)] / (1 - cosA) (1 + cosA)

= [sinA + sinAcosA + sinA - sinAcosA] / 1 - cos(sq) A

= 2sinA / sin(sq) A [From identity: sin(sq) A + cos(sq) A = 1]

= 2 / sin A

= 2 x 1 / sinA

=2 cosecA

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Answer 2

Answer:

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