Target Mathematics

1.25: Trigonometric identities

4PM1/2R/June/2024 — Question 11 · 12 marks

(a) Using a formula on page 2 show that cos⁡2A=2cos⁡2A−1\cos 2A = 2\cos^2 A - 1
(2)
(b) Hence show that (2cos⁡2A−1)2=cos⁡4A+12(2\cos^2 A - 1)^2 = \frac{\cos 4A + 1}{2}
(3)
The curve with equation y=sin⁡2x2+(2cos⁡2x−1)22+18y = \frac{\sin 2x}{2} + \frac{(2\cos^2 x - 1)^2}{2} + \frac{1}{8} has a stationary point PP in the range 0≤x≤π60 \leq x \leq \frac{\pi}{6}
(c) Find the exact coordinates of PP
(7)