# Thread: Trig question

1. ## Trig question

I'm having trouble with this question. Normally i would use auxiliary method but I'm having difficulty. Thanks in advance.

(i) Express 2cosθ + 2cos(θ + π∕3) in the form Rcos (θ + α), where R > 0 and, 0 < α < π/2

(ii) Hence, or otherwise, solve 2cosθ + 2cos(θ + π∕3) = 3, for 0 < α < 2π

2. ## Re: Trig question

Hint: use the identity

$\cos x + \cos y = 2 \cos \left(\frac{x+y}{2}\right)\cos \left(\frac{x-y}{2}\right)$

And note that

$\cos\left( \frac{\theta - \left(\theta + \frac{\pi}{3}\right)}{2}\right)$

is a constant.

3. ## Re: Trig question

Originally Posted by mj8
I'm having trouble with this question. Normally i would use auxiliary method but I'm having difficulty. Thanks in advance.

(i) Express 2cosθ + 2cos(θ + π∕3) in the form Rcos (θ + α), where R > 0 and, 0 < α < π/2

(ii) Hence, or otherwise, solve 2cosθ + 2cos(θ + π∕3) = 3, for 0 < α < 2π
you have to expand the second term first using your sum of angles and simplify before you use your usual auxiliary angle.

fan96 did suggest a faster method, though that formula isn't in the syllabus anymore.

4. ## Re: Trig question

Thanks!

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