Target Mathematics

2.29: Cosecant identity and mixed equations

0606/23/O/N/17 — Question 10 · 12 marks

(a)
Show that sinx1+cosx+1+cosxsinx=2cscx\dfrac{\sin x}{1 + \cos x} + \dfrac{1 + \cos x}{\sin x} = 2\csc x.
[3]
(b)(i)
Solve cot2y+cscy5=0\cot^{2} y + \csc y - 5 = 0 for 0°y360°0^{\degree} \le y \le 360^{\degree}.
[5]
(b)(ii)
Solve cos(2z+π4)=32\cos\left(2z + \tfrac{\pi}{4}\right) = -\tfrac{\sqrt{3}}{2} for 0zπ0 \le z \le \pi radians.
[4]