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

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Question 1136287: Prove that
tanA/(1 - cotA) + cotA/(1 - tanA) = (secAcosecA + 1)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!


Manipulating left side

tan%28A%29%2F%281+-+cot%28A%29%29+%2B+cot%28A%29%2F%281+-+tan%28A%29%29

=

=

=

factor numerator completely:
write it as

group





%28tan%28A%29%2B+cot%28A%29%2B1%29%281-tan%28A%29%29%29%281+-+cot%28A%29%29

then we have:
=....simplify
=tan%28A%29%2B+cot%28A%29%2B1
express tan%28A%29 and cot%28A%29 with sec%28A%29 and csc%28A%29

tan%28A%29=sec%28A%29%2Fcsc%28A%29
cot%28A%29=++csc%28A%29%2Fsec%28A%29
so we have
=sec%28A%29%2Fcsc%28A%29%2B+csc%28A%29%2Fsec%28A%29%2B1

=%28sec%5E2%28A%29%2Bcsc%5E2%28A%29%29%2F%28csc%28A%29sec%28A%29%29%2B1

factor numerator: sec%5E2%28A%29%2Bcsc%5E2%28A%29=%28csc%28A%29sec%28A%29%29%28sec%28A%29csc%28A%29+%29
so we have
=%28csc%28A%29sec%28A%29%29%28sec%28A%29csc%28A%29+%29%2F%28csc%28A%29sec%28A%29%29%2B1....simplify

=

=sec%28A%29csc%28A%29%2B1