Target Mathematics

3.61: Sec/cosec and compound-angle equations

0606/22/M/J/25 — Question 9 · 10 marks

(a)
Solve the equation 3 sec 3x=cosec 3x\sqrt{3}\,\mathrm{sec}\,3x = \mathrm{cosec}\,3x for −120∘⩽x⩽120∘-120^{\circ} \leqslant x \leqslant 120^{\circ}.
[5]
(b)
Solve the equation 2 cos(y+π3)+sin(y+π3)=sin y+cos y2\,\mathrm{cos}\left(y+\dfrac{\pi}{3}\right) + \mathrm{sin}\left(y+\dfrac{\pi}{3}\right) = \mathrm{sin}\,y + \mathrm{cos}\,y for 0⩽y⩽2π0 \leqslant y \leqslant 2\pi.
[5]