SOLUTION: prove this identity 1+ sin x/ cos x +cos x/ 1 + sin x = 2secx

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Question 1057128: prove this identity
1+ sin x/ cos x +cos x/ 1 + sin x = 2secx
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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prove this identity
1+ sin x/ cos x +cos x/ 1 + sin x = 2secx
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%281%2B+sin%28x%29%29%2Fcos%28x%29+%2Bcos%28x%29%2F%281+%2B+sin%28x%29%29 =  = %28%281%2Bsin%28x%29%29%5E2+%2B+cos%5E2%28x%29%29%2F%28cos%28x%29%2A%281%2Bsin%28x%29%29%29 = 

 =        ( <--- use sin%5E2%28x%29+%2B+cos%5E2%28x%29 = 1 )

= %282%2B2sin%28x%29%29%2F%28cos%28x%29%2A%281%2Bsin%28x%29%29%29 =  %282%2A%281%2Bsin%28x%29%29%29%2F%28cos%28x%29%2A%281%2Bsin%28x%29%29%29 =  = 2%2Fcos%28x%29 = 2*sec(x).


QED.