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The Humongous Book of Trigonometry Problems by W. Michael Kelley

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Squaring

With squares come Pythagorean identities

Note: Problems 11.23–11.24 refer to the equation cos x = sin x + 1.

11.23 Square both sides of the equation and apply a Pythagorean identity to identify three potential solutions on the interval 0 ≤ x < 2π.

When you square both sides of an equation, you run the risk of introducing extra “solutions” that are actually false. That’s true here, and you’ll pluck out that false “solution” in Problem 11.24.

Square both sides of the equation, as directed by the problem. Note that (sin x + 1)2 ≠ sin2 x + 12.

This equation contains two trigonometric expressions. Apply the technique demonstrated in Problems ...

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