WEBVTT

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Here is the problem: sin(x) plus cos(x) equals 1.

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Prove a trigonometric identity.

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Rewrite everything in terms of sin x and cos x. The expression already uses only sine and cosine.

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Left side in sine and cosine.

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Right side in sine and cosine.

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Subtract the sides and write the difference over a common denominator. The identity is true exactly when this numerator is zero for every value of the variable.

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Replace every cos squaredx with 1 minus sin squaredx and collect terms.

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The numerator is not zero, so the sides are not identical. At x equals 30°, the left side approximately 1.366025404 but the right side approximately 1.

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So the answer is This is not an identity: the two sides are not equal for all values.

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The difference of the sides does not reduce to 0. At x equals 30°, the left side approximately 1.366025404 but the right side approximately 1. The equation may still be true for particular values; solve it as an equation to find them.

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At x equals 30°, the left side approximately 1.366025404 but the right side approximately 1.