If then at is .

Question

If  then  at  is .

Canvas Classes · Accepted Answer

🧠 Recognise the Sum as a Single Cosine — Then  Collapses

We have . Find  at .

The expression inside  has the form  with , . This is the cosine of a sum:

,

where  and , so .

So each term is .

For  near :  is close to . So .

Thus .

.

At : .

🗺️ Working It Out

Rewrite the argument:

,

where  and . So .

So the th term in the sum is .

Locate  on the real line near . For  in a small neighbourhood of ,  is small, and  is close to , which is inside the principal range  of . So:

.

Theref

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