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# Evaluating trigonometric expressions...

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1. I am having trouble in evaluating the following expression:

Here is my working out:
Let's forget about the reciprocal for a moment.

let:
so:

Therefore (using Pythagorean Identities):

So:

(From )

Substituting the half angle formula:

Substituting back cos u:

Putting the original reciprocal back:

I am unsure how the book gives the following answer:

Can someone please tell me where I have gone wrong?
2. (Original post by Incongruous)
I am having trouble in evaluating the following expression:

Here is my working out:
Let's forget about the reciprocal for a moment.

let:
so:

Therefore (using Pythagorean Identities):

So:

(From )

Substituting the half angle formula:

Substituting back cos u:

Putting the original reciprocal back:

I am unsure how the book gives the following answer:

Can someone please tell me where I have gone wrong?
Multiply by .
Similar to how you would normally rationalise the denominator.
3. (Original post by B_9710)
Multiply by .
Similar to how you would normally rationalise the denominator.
Thank you

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