( 1 + sinx / cosx ) + ( cosx / 1 + sinx ) =
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(1 + sinx)(1 + sinx)/cosx(1 + sinx)
+
(cosx)(cosx)/(1 + sinx)(cosx) =
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(1 + sinx)^2 /cosx(1 + sinx)
+
(cosx)^2/cosx(1 + sinx) =
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1 + 2sinx + sin^2 x/cosx(1 + sinx)
+
cos^2 x/cosx(1 + sinx) =
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1 + sin^2 x + cos^2 x + 2sinx / cosx(1 + sinx) =
Hint :
Sin^2 x + Cos^2 x = 1
1 + 1 + 2sinx / cosx(1 + sinx) =
2 + 2sinx / cosx(1 + sinx) =
2(1 + sinx)/cosx(1 + sinx) =
( 1 + sinx) simplifies from the face and the denominator of the fraction
2/cosx
