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- Question 3, Exercise 9.1
- s 4x \leq 1 \,\, \forall \,\, x\in \mathbb{R} \\ \implies & -7\leq 7 \cos 4x \leq 7 \\ \end{align*} Thus do... b{R}$ As \begin{align*} & \theta \neq n\pi \\ \implies & \dfrac{\pi}{2} x \neq n\pi \\ \implies & x \neq 2n \end{align*} Hence domain of $y=\left\{x: x\in \mat... in{align*} & \theta \neq (2n+1)\frac{\pi}{2} \\ \implies & \pi x \neq (2n+1)\frac{\pi}{2} \\ \implies & x
- Question 1, Exercise 9.1
- & 4 \geq 2-2 \operatorname{Cos} \theta \geq 0 \\ \implies & 0 \leq 2-2 \operatorname{Cos} \theta \leq 4 \\ ... me{Sin} \theta \geq \dfrac{2}{3}-\dfrac{1}{2} \\ \implies & \dfrac{7}{6} \geq \dfrac{2}{3}-\dfrac{1}{2} \operatorname{Sin} \theta \geq \dfrac{1}{6} \\ \implies & \dfrac{1}{6} \leq \dfrac{2}{3}-\dfrac{1}{2} \op... torname{Sin}(3 \theta-7) \geq \dfrac{1}{5}-2 \\ \implies & \dfrac{11}{5} \geq \dfrac{1}{5}-2 \operatorname
- Question 2, Exercise 9.1
- & 1 \leq 4+3 \operatorname{Sin} \theta \leq 7 \\ \implies & 1 \geq \frac{1}{4+3 \operatorname{Sin}} \theta \geq \frac{1}{7} \\ \implies & \frac{1}{7} \leq \frac{1}{4+3 \operatorname{Sin... e{Sin(5 \theta-7)} \theta \leq 3 + \frac{2}{5}\\ \implies & \dfrac{13}{5} \geq \frac{1}{4+3 \operatorname{Sin(5 \theta-7)}} \theta \geq \dfrac{17}{5} \\ \implies & \dfrac{5}{13} \geq \frac{1}{4+3 \operatorname{S
- Question 2 and 3, Review Exercise
- \cos \theta=\sqrt{2}\sin \theta + \sin \theta \\ \implies & \cos \theta=(\sqrt{2}+1)\sin \theta\\ \implies & \sin \theta=\frac{1}{\sqrt{2}+1}\cos \theta ... (1) \en