(1 +sin x)/ (1-sin x) = (sec x + tan x)^2
2007-08-08 20:32:43 · 3 answers · asked by Stormy Knight 1 in Science & Mathematics ➔ Mathematics
(1 + sinx)^2 / (1-sin^2x)
(1 + 2sinx + sin^2x) / (cos^2x)
1/cos^2x + 2sinx/cos^2x + sin^2x/cos^2x
sec^2x + 2sinx/cosx * 1/cosx + tan^2x
sec^2x +2tanxsecx + tan^2x
(secx + tanx) ^2
= RHS
2007-08-08 20:58:38 · answer #1 · answered by sanjeewa 4 · 0⤊ 0⤋
start with LHS
(1 + sinx)^2 / (1-sin^2x)
(1 + 2sinx + sin^2x) / (cos^2x)
1/cos^2x + 2sinx/cos^2x + sin^2x/cos^2x
sec^2x + 2sinx/cosx * 1/cosx + tan^2x
sec^2x +2tanxsecx + tan^2x
(secx + tanx) ^2
= RHS!
2007-08-09 03:39:19 · answer #2 · answered by Anonymous · 0⤊ 0⤋
take the right side and change it to:
(1/cos x + sinx/cosx )^2 = (1 + sinx )^2 / (cosx)^2 =
(1 + sinx )^2 / (1-(sinx)^2) = (1 + sinx )^2 / (1-(sinx)(1+sinx))
reduce the fraction by (1+sinx) to get the left hand side.
2007-08-09 03:54:49 · answer #3 · answered by 037 G 6 · 0⤊ 0⤋