Trig question (1 Viewer)

[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

 

[fan96]

Hint: use the identity



And note that



is a constant.

 

[integral95]

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.

 

[mj8]

Thanks!