Need help! Given k = (1+sinx)/(cosx). How to prove 1/k = (1-sinx)/(cosx)?

Answer 1

k = (1+sinx) / (cosx)

1/k = cosx / (1+ sinx)

multiply by (1-sinx)

(cos x) * (1 - sinx)
------------------------
(1+sinx)(1-sinx)

(cox x) * (1 - sinx)
------------------------
1 - sin ^ 2 x ====> (a+b)(a-b)= a^2 - b^2

(cos x) * (1 - sin x)
-------------------------
cos^2 x ====> sin^2 x + cos^2 x = 1

(1 - sin x)
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cos x cancel cos x