SOLUTION: Prove that 1 - sin²A/(1 + cotA) - cos²A/(1 + tanA) = sinAcosA

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Question 1136236: Prove that
1 - sin²A/(1 + cotA) - cos²A/(1 + tanA) = sinAcosA
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


Manipulating left side
1+-+sin%5E2%28A%29%2F%281+%2B+cot%28A%29%29+-+cos%5E2%28A%29%2F%281+%2B+tan%28A%29%29

=

=

=

=

combine the fractions :

=1+%2Bsin+%28A%29%2Acos+%28A%29-cos%5E2%28A%29-sin%5E2%28A%29

=1+%2B+sin+%28A%29%2Acos+%28A%29-%28cos%5E2%28A%29%2Bsin%5E2%28A%29%29

=1+%2Bsin+%28A%29%2Acos+%28A%29+-1

=cross%281%29+%2Bsin+%28A%29%2Acos+%28A%29+-cross%281%29

= sin+%28A%29%2Acos+%28A%29-> proved