SOLUTION: prove trigonometric identity sin(x)/1-sin(x) + sin(x)/1+sin(x)= 2tan(x)sec(x)

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Question 604043: prove trigonometric identity sin(x)/1-sin(x) + sin(x)/1+sin(x)= 2tan(x)sec(x)
Answer by lwsshak3(11628) About Me  (Show Source):
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prove trigonometric identity
sin(x)/1-sin(x) + sin(x)/1+sin(x)= 2tan(x)sec(x)
**
Starting with left side:
sin/1-sin + sin/1+sin
=sin(1+sin+1-sin)/(1-sin)(1+sin)
=2sin/(1-sin^2)
=2sin/(cos^2)
=2sin/cos*1/cos
=2tansec
verified: left side=right side