Target Mathematics

2.17: Cotangent quadratic and fourth-power identity

0606/22/M/J/20 — Question 8 · 9 marks

(a)
Solve 3cot⁡2x−14csc⁡x−2=03\cot^{2} x - 14\csc x - 2 = 0 for 0°<x<360°0^{\degree} < x < 360^{\degree}.
[5]
(b)
Show that sin⁡4y−cos⁡4ycot⁡y=tan⁡y−2cos⁡ysin⁡y\dfrac{\sin^{4} y - \cos^{4} y}{\cot y} = \tan y - 2\cos y \sin y.
[4]