SOLUTION: Prove that tanA/(1 - cotA) + cotA/(1 - tanA) = (secAcosecA + 1)

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Question 1136237: Prove that
tanA/(1 - cotA) + cotA/(1 - tanA) = (secAcosecA + 1)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

here is other way, you might like it better
tan%28A%29%2F%281+-+cot%28A%29%29+%2B+cot%28A%29%2F%281+-+tan%28A%29%29




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=

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to have same denominators you can write sin%28A%29%28cos%28A%29+-+sin%28A%29%29 as -sin%28A%29%28sin%28A%29+-+cos%28A%29%29%29


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=


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use factoring cube difference rule in numerator

=...........simplify

=
=%28sin%5E2%28A%29%2B2sin%28A%29cos%28A%29%2Bcos%5E2%28A%29%29%2F%28sin%28A%29cos%28A%29%29
since sin%5E2%28A%29%2Bcos%5E2%28A%29=1
=%281%2B2sin%28A%29cos%28A%29%29%2F%28sin%28A%29cos%28A%29%29

=1%2F%28sin%28A%29cos%28A%29%29%2B%282sin%28A%29cos%28A%29%29%2F%28sin%28A%29cos%28A%29%29

=1%2F%28sin%28A%29cos%28A%29%29%2B2......use sec and csc to express sin and cos

=1%2F%28sin%28A%29cos%28A%29%29%2B2.....sin%28A%29=1%2Fcsc%28A%29,cos%28A%29=1%2Fsec%28A%29

=1%2F%28%281%2Fcsc%28A%29%29%281%2Fsec%28A%29%29%29%2B2

=1%2F%281%2Fcsc%28A%29sec%28A%29%29%2B2

=csc%28A%29sec%28A%29%2B2