Question

Prove that
tanA. +. cotA
------- ------- =1+secAcosec
1-cotA. 1-tanA​

Answer 1

Answer:

tanA/(1-cotA) +cotA/(1-tanA)

=tanA/(1–1/tanA) +cotA/(1-tanA)

=tan^2A/(tanA-1) +cotA/(1-tanA)

=-tan^2A/(1-tanA) +cotA/(1-tanA)

=(-tan^2A+cotA)/(1-tanA)

=(-tan^2A+1/tanA)/(1-tanA)

=(-tan^3A+1)/tanA(1-tanA)

=(1-tan^3A)/tanA(1-tanA)

=(1-tanA)(1+tanA+tan^2A)/tanA(1-tanA)

=(1+tanA+tan^2A)/tanA

=(1+tan^2A+tanA)/tanA

=(sec^2A+tanA)/tanA

=sec^2A/tanA +tanA/tanA

=1/cos^2AtanA+1

=cosA/cos^2AsinA+1

=1/cosAsinA+1

=secAcosecA+1

Step-by-step explanation:

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