Target Mathematics

3.110: Sec identity and equation

0606/21/O/N/25 — Question 4 · 6 marks

(a)
Show that 1−sin xcos x+cos x1−sin x=2 sec x\dfrac{1-\mathrm{sin}\,x}{\mathrm{cos}\,x}+\dfrac{\mathrm{cos}\,x}{1-\mathrm{sin}\,x}=2\,\mathrm{sec}\,x.
[3]
(b)
Hence solve the equation 1−sinθ2cosθ2+cosθ21−sinθ2=3\dfrac{1-\mathrm{sin}\tfrac{\theta}{2}}{\mathrm{cos}\tfrac{\theta}{2}}+\dfrac{\mathrm{cos}\tfrac{\theta}{2}}{1-\mathrm{sin}\tfrac{\theta}{2}}=3 for 0∘⩽θ⩽720∘0^{\circ}\leqslant \theta\leqslant 720^{\circ}.
[3]