1. ## Challenging Trigometry Question

Hi Math community,

I need help for 12(ii). I have tried many times but still can't get it. Can any kind soul please help?

2. ## Re: Challenging Trigometry Question

Hey mathstudent111.

Have you tried expanding the two expressions for s^2 and collecting terms?

3. ## Re: Challenging Trigometry Question

from part (i) ...

$s^2 = 2+4\sin^2{t}+4\sin{t}\cos{t}$

using double angle identities ...

$s^2 = 2 + 4\left[\dfrac{1-\cos(2t)}{2}\right] + 2\sin(2t)$

$s^2 = 4 - 2\left[\cos(2t)-\sin(2t)\right]$

$s^2 = 4 + \sqrt{2} \left[\cos(2t) \cdot \dfrac{\sqrt{2}}{2} - \sin(2t) \cdot \dfrac{\sqrt{2}}{2}\right]$

$s^2 = 4 + \sqrt{2} \left[\cos(2t) \cos\left(\dfrac{\pi}{4}\right) - \sin(2t) \cdot \sin\left(\dfrac{\pi}{4}\right) \right]$

$s^2 = 4 + \sqrt{2} \cos\left(2t + \dfrac{\pi}{4}\right)$