SOLUTION: prove (1/1+cosx)+(1/1-cosx)=2csc^2

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Question 1128175: prove (1/1+cosx)+(1/1-cosx)=2csc^2
Found 2 solutions by MathLover1, Boreal:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

prove 1%2F%281%2Bcos%28x%29%29%2B1%2F%281-cos%28x%29%29=2csc%28x%29%5E2+

start with left side
1%2F%281%2Bcos%28x%29%29%2B1%2F%281-cos%28x%29%29+



=%281-cos%28x%29%2B1%2Bcos%28x%29%29%2F%28%281%2Bcos%28x%29%29%281-cos%28x%29%29%29

=2%2F%28%281%2Bcos%28x%29%29%281-cos%28x%29%29%29

=2%2F%281-cos%28x%29%5E2%29

=2%2F%281-%281-sin%28x%29%5E2%29%29

=2%2F%281-1%2Bsin%28x%29%5E2%29%29

=2%2F%28sin%28x%29%5E2%29%29..........use identity sin%28x%29%5E2=1%2Fcsc%5E2%28x%29

=2%2F%281%2Fcsc%5E2%28x%29%29

=2csc%5E2%28x%29


Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
(1/1+cosx)+(1/1-cosx)=2csc^2=2/sin^2 x=2/(1-cos^2x)
common denominator on left is (1+cos x)(1-cos x) which is 1-cos^2 x
the numerator will become 1-cos x+1+cos x or 2
and the left side becomes 2/(1- cos^2 x)