SOLUTION: Prove that: Cosx/1-sinx + 1-sinx/cosx = 2secx

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Question 1040632: Prove that:
Cosx/1-sinx + 1-sinx/cosx = 2secx
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Grouping symbols are very important. Guessing might suggest where to include them, their placement should have been already included with the request for help.


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I figured out what your actual given equation is, and used one definition and one basic identity and did the proof on paper. My proof used seven steps. Most of the work is simple algebra. The identity used was cos%5E2%28x%29=1-sin%5E2%28x%29, definition sec%28x%29=1%2Fcos%28x%29, and Difference of Squares %281-sin%28x%29%29%281%2Bsin%28x%29%29=1-sin%5E2%28x%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Prove that:
Cosx/1-sinx + 1-sinx/cosx = 2secx


 ------- Multiplying left-side by LCD, (1 - sin x)(cos x)

 

 

 

%281+-+2sin+%28x%29+%2B+1%29%2F%281+-+sin+%28x%29%28cos+%28x%29%29%29 ----- Substituting 1 for cos%5E2+%28x%29+%2B+sin%5E2+%28x%29

%282+-+2sin+%28x%29%29%2F%281+-+sin+%28x%29%28cos+%28x%29%29%29 

2%281+-+sin+%28x%29%29%2F%281+-+sin+%28x%29%28cos+%28x%29%29%29_____2cross%28%281+-+sin+%28x%29%29%29%2Fcross%281+-+sin+%28x%29%29cos+%28x%29_______2+%2A+%281%2Fcos+%28x%29%29 = highlight_green%282+%2A+sec+%28x%29%29 (Same as right side)