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- Question 2, Exercise 8.1
- , Islamabad, Pakistan. ===== Question 2(a)===== Find the exact value of $\cos 15^{\circ}$ by using $\c... \cos 15^{\circ}=\dfrac{\sqrt{3}+1}{2\sqrt{2}}$ to find $\cos 165^{\circ}$ by using $\cos \left(180^{\cir... \cos 15^{\circ}=\dfrac{\sqrt{3}+1}{2\sqrt{2}}$ to find $\cos 345^{\circ}$ by using $\cos \left(360^{\cir... circ = \dfrac{\sqrt{3}+1}{2\sqrt{2}}$. Now, let's find $\cos 345^\circ$. \begin{align*} \cos 345^\circ &
- Question 1, Exercise 8.1
- , Islamabad, Pakistan. ===== Question 1(i)===== Find the value of $\cos (\alpha \pm \beta), \sin (\alp... ) =-\tan 60^\circ$ GOOD ===== Question 1(ii)===== Find the value of $\cos (\alpha \pm \beta), \sin (\alp... qrt{3} \end{align*} ===== Question 1(iii)===== Find the value of $\cos (\alpha \pm \beta), \sin (\alp... t{3}}{3} \end{align*} ===== Question 1(iv)===== Find the value of $\cos (\alpha \pm \beta), \sin (\alp
- Question 3, Exercise 8.1
- , Islamabad, Pakistan. ===== Question 3(a)===== Find the exact value of $\cos 120^{\circ}$ by using $\... 1}{2}. \end{align*} GOOD ===== Question 3(b)===== Find the exact value of $\sin 120^{\circ}$ and then $\... -\sqrt{3}. \end{align*} ===== Question 3(c)===== Find the exact value of $\cos 75^{\circ}$ by using $\c... \cos 75^{\circ}=\dfrac{\sqrt{3}-1}{2\sqrt{2}}$ to find $\cos 105^{\circ}$ by using $\cos \left(180^{\cir
- Question 4 Exercise 8.2
- d, Islamabad, Pakistan. =====Question 4(i)===== Find (a) $\sin 2 \theta$ (b) $\cos 2 \theta$ %%(c)%% $... 1}{2}} \end{align*} GOOD =====Question 4(ii)===== Find (a) $\sin 2 \theta$ (b) $\cos 2 \theta$ %%(c)%% $... {3}{2}}. \end{align*} =====Question 4(iii)===== Find (a) $\sin 2 \theta$ (b) $\cos 2 \theta$ %%(c)%% $... ac{1}{7}}. \end{align*} =====Question 4(iv)===== Find (a) $\sin 2 \theta$ (b) $\cos 2 \theta$ %%(c)%% $
- Question 6 Exercise 8.2
- Question 6(i)===== Use a double-angle identity to find exact values for the expression: $\sin 15^{\circ}... uestion 6(ii)===== Use a double-angle identity to find exact values for the expressions: $\cos ^{2} 15^{... estion 6(iii)===== Use a double-angle identity to find exact values for the expression: $1-2 \sin ^{2}\l... uestion 6(iv)===== Use a double-angle identity to find exact values for the expression: $2 \cos ^{2}\lef
- Question 5 Exercise 8.2
- d, Islamabad, Pakistan. =====Question 5(i)===== Find exact values for $\sin \theta$, $\cos \theta$ and... 4}{3}} \end{align*} GOOD =====Question 5(ii)===== Find exact values for $\sin \theta, \cos \theta$ and $... 4}{3}}. \end{align*} =====Question 5(iii)===== Find exact values for $\sin \theta, \cos \theta$ and $... c{15}{8}}. \end{align*} =====Question 5(iv)===== Find exact values for $\sin \theta, \cos \theta$ and $
- Question 9, Exercise 8.1
- frac{1}{\sqrt{2}}$ and $\cos \beta=-\dfrac{3}{5}$ find: $\sin (\alpha \pm \beta)$ ** Solution. ** Giv... \frac{1}{\sqrt{2}}$ and $\cos \beta=-\frac{3}{5}$ find: $\cos (\alpha \pm \beta)$ ** Solution. ** Give... \frac{1}{\sqrt{2}}$ and $\cos \beta=-\frac{3}{5}$ find: $\tan (\alpha \pm \beta)$ ** Solution. ** Give
- Question 14, Exercise 8.1
- angle that the longer wire makes with the ground. Find $\sin \theta$ and $\cos \theta$.\\ **c.** Find the cosine of the angle between the wires where they meet at the ground. **d.** Find, to the nearest degree, the measure of the angle
- Question 1, 2 and 3 Exercise 8.2
- a$ when $\theta$ is plotted in standard position. Find $\cos 2 \theta$ and $\sin 2 \theta$ and determine... ==== If $\sin \alpha=y$ and $\alpha$ lies in QII. Find expressions for $\sin 2 \alpha$, $\cos 2 \alpha$ ... =====Question 3===== Use a half angle formula to find the exact value of $\cos 15^{\circ}$. ** Solutio
- Question 2, Review Exercise
- 3}$ where $\theta$ is obtuse and $\phi$ is acute. Find the values of $\sin (\theta-\phi)$. ** Solution.... 3}$ where $\theta$ is obtuse and $\phi$ is acute. Find the values of $\tan (\theta-\phi)$. ** Solution.... 3}$ where $\theta$ is obtuse and $\phi$ is acute. Find the values of: $\tan (\theta+\phi)$ ** Solution.
- Question 5 and 6, Exercise 8.1
- c{5}{12}$ with terminal side of an angles in QII, find $\cos (\alpha+\beta)$ and $\cos (\alpha-\beta)$. ... ac{15}{8}$ with terminal side of $\beta$ in QIII, find \\ (i) $\sin(\alpha-\beta)$ (ii) $\cos(\alpha-\be
- Question 4, Review Exercise
- d, Islamabad, Pakistan. =====Question 4(i)===== Find the values of: $\dfrac{1+\tan 15^{\circ}}{1-\tan ... \\ =&1.732 \end{align*} =====Question 4(ii)===== Find the values of: $\cos 70^{\circ} \cdot \cos 20^{\c
- Question 7, Exercise 8.1
- pha=\dfrac{12}{13}$ and $\tan \beta=\dfrac{4}{3}$ find \\ (i) $\sin(\alpha+\beta)$ (ii) $\cos(\alpha+\be
- Question 8, Exercise 8.1
- ac{12}{13}$, where $\dfrac{3 \pi}{2}<\beta<2 \pi$ find: \\ (i) $\csc (\alpha+\beta)$ (ii) $\sec (\alpha+
- Question 5 and 6, Review Exercise
- ard, Islamabad, Pakistan. =====Question 5===== Find the values of $\tan \theta$ when $\tan \left(\the