Question

Prove that: tanA/1-cotA+cotA/1-tanA=1+secA×cosec

Answer 1

Step-by-step explanation:

tanA/1-cotA+cotA/1-tanA

=(sinA/cosA)sinA/sinA-cosA + (cosA/sinA)cosA/cosA-sinA

=sin²A/cosA(sinA-cosA)+cos²A/sinA(cosA-sinA)

=sin²A/cosA(sinA-cosA)-cos²A/sinA(sinA-cosA)

=sin³A-cos³A/cosAsinA(sinA-cosA)

=(sinA-cosA)(sin²A+sinAcosA+cos²A)/cosAsinA(sinA-cosA)

=(sinA-cosA)(1+sinAcosA)/cosAsinA(sinA-cosA)

=1+sinAcosA/cosAsinA

=secAcosecA+1

=1+secAcosecA

Answer 2

Answer:

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