Question

simplify (cosx/1+sinx)+(1+sinx/cosx)

Trigonometric equation and identitie
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asked 2020-12-28

simplify \((\cos x/1+\sin x)+(1+\sin x/\cos x)\)

Answers (1)

2020-12-29

\((\cos x/1+\sin x)+(1+\sin x/\cos x) = (\cos x/1+\sin x) +((\cos x+\sin x)/\cos x)\)
\(= ( \cos^2x + (1+\sin x)(\cos x+\sin x) )/ \cos x(1+\sin x)\)
\(= ( \cos^2x + \cos x + \sin x + \sin x\cos x +\sin^2x ) / \cos x(1+\sin x)\)
\(= (1+\cos x+\sin x+\sin x\cos x) / \cos x(1+\sin x)\)
\(= ( 1+\cos x+\sin x(1+\cos x) ) / \cos x(1+\sin x)\)
\(= (1+\cos x)(1+\sin x) / \cos x(1+\sin x)\)
\(= (1+\cos x) / \cos x\)
\(= 1+\sec x\)

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