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题目
单项选择题
sec 4 𝑥 − 1 tan 2 𝑥 can be simplified as: Hint: sec 2 𝑥 = 1 + tan 2 𝑥
选项
A.2
+
sec
2
𝑥
B.2
+
tan
2
𝑥
C.2
+
cos
2
𝑥
D.1
+
cot
2
𝑥
查看解析
标准答案
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思路分析
The problem presents a trigonometric simplification task involving secant and tangent expressions. I will evaluate each answer option by applying standard identities and algebraic manipulation, then discuss why each option does or does not align with the given expression.
Option 1: 2 + sec^2 x
- If the original expression simplifies to 2 + sec^2 x, then after simplification the result would have a sec^2 x term plus a constant 2. To verify this, one would expect the algebra to naturally produce a constant term and a sec^2 x term without any other functions (like tan^2 x or cos^2 x) remaining. However, based on common identities (for example, sec^2 x = 1 + tan^2 x), manipulating expressions like sec^4 x ......Login to view full explanation登录即可查看完整答案
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类似问题
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.]
Which expression is equivalent to ?
Which expression correctly expands ?
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)
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