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A detailed explanation of the urgency of high school mathematics
The first step: double-angle mathematics, cos2x=cos? x-sin？ x= 1-2sin？ x

Step 2: Substitute into the original formula to simplify, f(x)=-2sin? x+2sinx+ 1

Step 3: substitution method, let t=sinx-1≤t≤ 1, then f(t)=-2t? +2t+1(-1≤ t ≤1) and then find the maximum and minimum of this quadratic function.

Step 4: Find the maximum value of quadratic function by mirror method, and get the minimum value of -3 and the maximum value of 3/2. Answer C.

Please pay attention to "Ping Liu Mathematics"

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