Question

Verify the identity.
cos x/1+sin x = sec x - tanx
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Answer 1

See below for proof

Explanation:

`\displaystyle (\cos x)/(1+\sin x)=(\cos x(1-\sin x))/((1+\sin x)(1-\sin x))\\\\(\cos x)/(1+\sin x)=(\cos x(1-\sin x))/(1-\sin^2x)\\\\(\cos x)/(1+\sin x)=(\cos x(1-\sin x))/(\cos^2x)\\\\(\cos x)/(1+\sin x)=(1-\sin x)/(\cos x)\\\\(\cos x)/(1+\sin x)=(1)/(\cos x)-(\sin x)/(\cos x)\\\\(\cos x)/(1+\sin x)=\sec x-\tan x`