# Thread: [SOLVED] How to calculate integral of sqrt( 2 - 2cos(t) ) ?

1. ## [SOLVED] How to calculate integral of sqrt( 2 - 2cos(t) ) ?

I want to evaluate the integral of this, but I am having some difficulty simplyfing the expresion to integrate. $\sqrt{2 - 2\cos t} = \sqrt{2} \sqrt{1-\cos t}$ and I don't know what else to do...

Any help is appreciated.

Thanks.

2. $\cos t=1-2\sin ^{2}\frac{t}{2}.$

3. Originally Posted by Krizalid
$\cos t=1-2\sin ^{2}\frac{t}{2}.$
Thanks for your reply. That does work. But, may I ask how did you know that? Certainly there's a way do deduce that expression.

Thanks.

4. Of course, just consider the double angle formula for the cosine, then $\cos2t=1-2\sin^2t,$ then i just put $t\mapsto\frac t2.$

5. Originally Posted by Krizalid
Of course, just consider the double angle formula for the cosine, then $\cos2t=1-2\sin^2t,$ then i just put $t\mapsto\frac t2.$
I have never used that trigonometric identity before, but now am aware of it. Thanks for your help.

Cheers.

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### integral 1-2cos t

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