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- BullwinkleLv 77 years agoFavorite Answer
(1 - sin x)/cos x = cos x/(1 + sin x)

work on LHS...

multiply numerator and denominator by (1 + sin x)/(1 + sin x) [which is equal to ONE !]

[(1 - sin x)(1 + sin x)]/[cos x(1 + sin x)] = [1 - sin^2 x] / [cos x(1 + sin x)]

1 - sin^2 x = cos^2 x

so...

(cos^2 x)/[cos x(1 + sin x)] = (cos x) / (1 + sin x) RHS

QED

- JOS JLv 77 years ago
(1 - Sin[x])/Cos[x] = Cos[x]/(1 + Sin[x])

-Sec[x] (-1 + Sin[x]) = Cos[x]/(1 + Sin[x])

Sec[x] (1 - Sin[x]) (1 + Sin[x]) = Cos[x]

Sec[x] (1 - Sin[x]^2) = Cos[x]

Cos[x] = Cos[x]

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