Prove that $$$ \sin 2 \theta(\operatorname{cosec} \theta-\sec \theta) \equiv \sqrt{8} \cos \left(\theta+\frac{1}{4} \pi\right) . $$$ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_21 Year：2020 Question No：6(a)

Answer:

Express left-hand side in terms of $\sin \theta$ and $\cos \theta$
Obtain $2 \cos \theta-2 \sin \theta$
Attempt to express $a \cos \theta+b \sin \theta$ in $R \cos (\theta+\beta)$ form
Confirm $R=\sqrt{8} \quad \mathrm{AG}$
Carry out necessary trigonometry and confirm $\frac{1}{4} \pi \quad \mathrm{AG}$

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