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Question
If y = `(2sinalpha)/(1 + cosalpha + sinalpha)`, then prove that `(1 - cosalpha + sinalpha)/(1 + sinalpha)` = y
Solution
`(2sinalpha)/(1 + cosalpha + sinalpha) = (2sinalpha)/((1 + sinalpha) + cosalpha)`
= `(2sinalpha)/((1 + sin alpha) + cos alpha) xx ((1 + sinalpha) - cosalpha)/((1 + sinalpha) - cosalpha)`
y = `(2sinalpha(1 - cosalpha + sinalpha))/((1 + sinalpha)^2 - cos^2alpha)`
= `(2sinalpha(1 - cosalpha + sinalpha))/(1 + 2sinalpha + sin^2alpha - cos^2alpha)`
= `(2sinalpha(1 - cosalpha + sinalpha))/(1 + 2sinalpha + sin^2alpha - (1 - sin^2alpha))`
= `(2sinalpha(1 - cosalpha + sinalpha))/(1 + 2sinalpha + sin^2alpha - 1 - sin^2alpha)`
= `(2sinalpha(1 - cosalpha + sinalpha))/(2sinalpha + 2sin^2alpha)`
= `(2sinalpha(1 - cosalpha + sinalpha))/(2sinalpha(1 + sinalpha))`
y = `(1 - cosalpha + sinalpha)/(1 + sinalpha)`
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