Year 12s: what will be the first way you research your future options? >>

Identity question

In a worked example I have of an integration it states the integral of (cosx)^2 = the integral of (1 + cos2x)/2

How is this equality reached?

Is this a known identity, (cosx)^2 = (1 + cos2x)/2 ?

Thank you.

Reply 1

raheem94

Original post by little pixie

cos2x = 2cos^2x -1

Rearrange the above expression to get

cos^2x = \dfrac{1+cos2x}{2}

(edited 11 years ago)

Reply 2

little pixie

Thanks raheem94.

So the first equation you have stated above, is that a well known identity? I don't think I'm aware of that one.

Reply 3

Zii

Original post by little pixie

Thanks raheem94.

So the first equation you have stated above, is that a well known identity? I don't think I'm aware of that one.

You must be aware of

\cos^2(x) + \sin^2(x) = 1

and

\cos^2(x) - \sin^2(x) = \cos(2x)

.

Combine these.

Reply 4

TenOfThem

Original post by little pixie

Thanks raheem94.

So the first equation you have stated above, is that a well known identity? I don't think I'm aware of that one.

Standard re-arrangement of Cos2x

Standard integration method

If you are not aware then you have not been well taught (or you have not been attentive)

Quick Reply

Latest

Articles for you

Student finance – how to apply

The Student Room community guidelines

What is an LLM and how could it benefit your career?

Powerful questions business students forget to ask their career advisers

Identity question

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you