WEBVTT

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Here is the problem: tan(x)cos(x).

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Simplify a trigonometric expression.

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Rewrite everything in terms of sin x and cos x. Identities used:.

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Combine into a single fraction.

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Use sin squaredx plus cos squaredx equals 1 (replace cos squared with 1 minus sin squared) and cancel common factors.

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Recognise a standard form. Cross-multiplying and reducing with sin squared plus cos squared equals 1 shows the difference is exactly 0.

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So the answer is sin(x).

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tan(x)cos(x) simplifies to sin(x) for every x where the original expression is defined.

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Numeric spot check: the original expression and the result agree at sample values of x.