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How to do the seventh question, engineering mathematics. . . .
You mean the one in the middle Is it the one under the flip property? Cos and sin?

Well, use Euler's formula: e iwt = coswt+I * sinwt, and you can get it by substituting this into the right.

Of course, it can also be obtained by substituting: cos wt = 1/2 * (e iwt+e (-iwt)) into the formula on the left.

The premise is to write the Fourier transform completely after writing, and you will know why.