Question

Please help me verify: [(cosx/(1+sinx)=(secx)-(tanx)]

Answer 1

Multiply the fraction on the left by (1-sinx)/(1-sin x)

Answer 2

okay i will try it now

Answer 3

Okay so, I got to [(sinx)(cosx)-(cosx) / (sinx)+(cos^2x)-(sinx) I can see how maybe -(cosx)/-(sinx) can eventually be -tanx? I can't see how to get (secx)?

Answer 4

\[\frac{\cos x}{1+\sin x}\times \frac{1-\sin x}{1-\sin x}=\frac{\cos x(1-\sin x)}{1- \sin ^2x}=\]
\[\frac{\cos x(1-\sin x)}{\cos ^2x}=\frac{1-\sin x}{\cos x}=\frac{1}{\cos x}-\frac{ \sin x}{\cos x}=\sec x-\tan x\]