We will apply the Pythagorean identity of sin 2 𝑥 + cos 2 𝑥 = 1 when we notice any of the following in a trigonometric expression or equation: (Select ALL correct answers)Multiple choice
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Question text Each student below analyzes a proposed trigonometric expression and explains their reasoning.Match each student’s reasoning to the explanation that best fits their thinking. Student 1:I was asked to evaluate .I tested it using and , and the two sides were not equal. I tried other values too and got the same result. I believe this expression is never true.Answer 1 Question 23[select: , The student was correct; the expression is never true. Multiple test cases using different values always yield unequal results., The student analysis was incorrect; the expression is always true because it is a valid trigonometric identity., The student analysis was incorrect; the expression is sometimes true. It holds for some distinct values of x and y, but is unequal for other values.] Student 2:I was asked to verify .I recognized the numerator as based on the Pythagorean identity, so the left side of the expression becomes .I now realize this means the expression is never true.Answer 2 Question 23[select: , The student's analysis was incorrect; the expression is always true because the numerator is equivalent to sin^2(x), not -sin^2(x)., The student's analysis was incorrect; the expression is sometimes true because it holds for specific values of x, but fails for most other values., The student was correct; the expression is never true since the left side simplifies to -1, which is never equal to the right side.] Student 3:I was asked to evaluate .I tested it using , and both sides came out equal. I concluded the expression is always true.Answer 3 Question 23[select: , The student was correct; the expression is always true for all values of x ., The student analysis was incorrect; the expression is sometimes true; when different values for x are tested, the two sides are not equal., The student analysis was incorrect; the expression is never true for any value of x.]
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