Question

prove cosx/1+sinx=1-sinx/cosx

Answer 1

cosx/(1-sinx) = (1+sinx)/cosx
=cosx/(1-sinx)
=(cosx(1+sinx))/((1-sinx)(1+sinx))
=(cosx+cosxsinx)/(1-sin²x)
=(cosx+cosxsinx)/(cos²x)
=(1+sinx)/cosx

Answer 2

\[{\cos x \over1+\sin x}={1-\sin x \over \cos x}\]

Answer 3

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Answer 4

\[LHS\\={\cos x \over 1+ \sin x}\\={\cos x \over 1+ \sin x}\times {\left( 1-\sin x \right)\over\left( 1-\sin x \right)}\]

Answer 5

\[={\cos x\left( 1-\sin x \right)\over 1-\sin^2x}\]

Answer 6

\[={\cos x\left( 1-\sin x \right)\over \cos^2x} \\={1-\sin x \over \cos x}\\=RHS\]