Geometry Quiz
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TRIGONOMETRIC IDENTITIES
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In the diagram, △ABC\triangle ABC is a right triangle with right angle at CC. The angle at AA is labeled θ\theta. The hypotenuse AB‾\overline{AB} is labeled 11, the leg AC‾\overline{AC} (adjacent to θ\theta) is labeled cos⁡θ\cos\theta, and the leg BC‾\overline{BC} (opposite θ\theta) is labeled sin⁡θ\sin\theta. Which reasoning proves sin⁡2θ+cos⁡2θ=1\sin^2\theta+\cos^2\theta=1 for this setup (and thus for all θ\theta where the triangle is defined)? Figure accompanying this question
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