Solved: "Simplify the expression sec⁡xsin⁡x−sin⁡xcos⁡x"

Globokim8

Answered question

2020-11-01

Simplify the expression

\frac{\sec x}{\sin x} - \frac{\sin x}{\cos x}

Sally Cresswell

Skilled2020-11-02Added 91 answers

\sec x = \frac{1}{\cos x}

\frac{\frac{1}{\cos x}}{\sin x} - \frac{\cos x}{\sin x}

\frac{\frac{1}{\cos x} - \cos x}{\sin x}

\frac{\frac{1}{\cos x} - \frac{\cos^{2} x}{\cos x}}{\sin x}

\frac{1 - \frac{\cos^{2} x}{\cos x}}{\sin x}

\cos^{2} x + \sin^{2} x = 1 \to \sin^{2} x = 1 - \cos^{2} x

\frac{\frac{\sin^{2} x}{\cos x}}{\sin x} \to (\frac{\sin^{2} x}{\cos x}) • (\frac{1}{\sin x})

= \frac{\sin^{2} x}{\sin x} \cos x

\frac{\sin x}{\cos x} = \tan x

= \tan x

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