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- Question 1, Exercise 8.1
- Question 2, Exercise 8.1
- Question 3, Exercise 8.1
- Question 4, Exercise 8.1
- Question 5 and 6, Exercise 8.1
- Question 7, Exercise 8.1
- Question 8, Exercise 8.1
- Question 9, Exercise 8.1
- Question 10, Exercise 8.1
- Question 11, Exercise 8.1
- Question 12, Exercise 8.1
- Question 13, Exercise 8.1
- Question 14, Exercise 8.1
- Question 1, 2 and 3 Exercise 8.2
- Question 4 Exercise 8.2
- Question 5 Exercise 8.2
- Question 6 Exercise 8.2
- Question 7 Exercise 8.2
- Question 8(i, ii & iii) Exercise 8.2
- Question 8(iv, v & vi) Exercise 8.2
- Question 8(vii, viii & ix) Exercise 8.2
- Question 8(x, xi & xii) Exercise 8.2
- Question 8(xiii, xiv & xv) Exercise 8.2
- Question 8(xvi, xvii & xviii) Exercise 8.2
- Question 8(xix, xx, xxi & xxii) Exercise 8.2
- Question 1(i, ii, iii & iv) Exercise 8.3
- Question 1(v, vi, vii & viii) Exercise 8.3
- Question 1(ix, x & xi) Exercise 8.3
- Question 2(i, ii, iii, iv and v) Exercise 8.3
- Question 3(i, ii, iii, iv & v) Exercise 8.3
- Question 3(vi, vii, viii, ix & x) Exercise 8.3
- Question 3(xi, xii & xiii) Exercise 8.3
- Question 4 Exercise 8.3
- Question 1, Review Exercise
- Question 2, Review Exercise
- Question 3, Review Exercise
- Question 4, Review Exercise
- Question 5 and 6, Review Exercise
- Question 7, Review Exercise
- Question 8, Review Exercise
- Question 9, Review Exercise
- Question 10, Review Exercise
Fulltext results:
- Question 10, Exercise 8.1
- ====== Question 10, Exercise 8.1 ====== Solutions of Question 10 of Exercise 8.1 of Unit 08: Fundamenta... ft(\dfrac{\pi}{2}-\alpha\right)=\cos \alpha$ ** Solution. ** \begin{align*} L.H.S & = \sin \left(\fr... === Verify: $\cos (\pi-\alpha)=-\cos \alpha$ ** Solution. ** \begin{align*} L.H.S & = \cos(\pi - \al... frac{1}{\sqrt{2}}(\cos \alpha-\sin \alpha)$ ** Solution. ** \begin{align*} L.H.S &= \cos \left(\alp
- Question 11, Exercise 8.1
- ====== Question 11, Exercise 8.1 ====== Solutions of Question 11 of Exercise 8.1 of Unit 08: Fundamenta... ht) \cos \left(270^{\circ}-\lambda\right)}=1$ ** Solution. ** \begin{align*} L.H.S & = \dfrac{\sin \l... ght)+\cos \left(90^{\circ}+\alpha\right)}=-1$ ** Solution. ** \begin{align*} L.H.S & = \frac{\sin \le... \sin (\alpha+\beta)}{\cos \alpha \cos \beta}$ ** Solution. ** \begin{align*} L.H.S & = \tan \alpha+\t
- Question 3, Exercise 8.1
- ====== Question 3, Exercise 8.1 ====== Solutions of Question 3 of Exercise 8.1 of Unit 08: Fundamental ... nd $\cos \left(90^{\circ}+30^{\circ}\right)$. ** Solution. ** \begin{align*} \cos 120^{\circ} & = \co... sin 120^{\circ}$ and then $\tan 120^{\circ}$. ** Solution. ** \begin{align*} \sin 120^{\circ} & = \si... g $\cos \left(120^{\circ}-45^{\circ}\right)$. ** Solution. ** \begin{align*} \cos 75^{\circ} & = \cos
- Question 4, Exercise 8.1
- ====== Question 4, Exercise 8.1 ====== Solutions of Question 4 of Exercise 8.1 of Unit 08: Fundamental ... ta \cos 3 \theta-\sin 6 \theta \sin 3 \theta$ ** Solution. ** \begin{align*} & \cos 6 \theta \cos 3 \... a \cos 2 \theta+\sin 7 \theta \sin 2 \theta$. ** Solution. ** \begin{align*} & \cos 7 \theta \cos 2 \... 3}\right) \sin \left(\frac{\theta}{6}\right)$ ** Solution. ** \begin{align*} & \sin \left(\frac{\thet
- Question 4 Exercise 8.2
- ====== Question 4 Exercise 8.2 ====== Solutions of Question 4 of Exercise 8.2 of Unit 08: Fundamental o... a=\frac{3}{5}$ where $0<\theta<\frac{\pi}{2}$ ** Solution. ** Given: $\cos\theta=\dfrac{3}{5}$ where ... ac{12}{5}$ where $\pi<\theta<\frac{3 \pi}{2}$ ** Solution. ** Given: \(\tan \theta = \frac{12}{5}\) w... {7}{25}$ where $\frac{3 \pi}{2}<\theta<2 \pi$ ** Solution. ** Given: \(\sin \theta = -\frac{7}{25}\)
- Question 1, Exercise 8.1
- ====== Question 1, Exercise 8.1 ====== Solutions of Question 1 of Exercise 8.1 of Unit 08: Fundamental ... ngles. $\alpha=180^{\circ}, \beta=60^{\circ}$ ** Solution. ** Given: $\alpha=180^{\circ}$, $\beta=60^... angles. $\alpha=60^{\circ}, \beta=90^{\circ}$ ** Solution. ** Given: \(\alpha = 60^\circ\), \(\beta =... ngles. $\alpha=180^{\circ}, \beta=30^{\circ}$ ** Solution. ** Given: $\alpha = 180^\circ$, $\beta = 3
- Question 6 Exercise 8.2
- ====== Question 6 Exercise 8.2 ====== Solutions of Question 6 of Exercise 8.2 of Unit 08: Fundamental o... expression: $\sin 15^{\circ} \cos 15^{\circ}$ ** Solution. ** We have double-angle identity: $$\sin 2... : $\cos ^{2} 15^{\circ}-\sin ^{2} 15^{\circ}$ ** Solution. ** We have double-angle identity: $$\cos^2... on: $1-2 \sin ^{2}\left(\frac{\pi}{8}\right)$ ** Solution. ** We have a double-angle identity: $$\cos
- Question 2(i, ii, iii, iv and v) Exercise 8.3
- stion 2(i, ii, iii, iv and v) Exercise 8.3 ====== Solutions of Question 2(i, ii, iii, iv and v) of Exer... function: $\sin 70^{\circ} + \sin 30^{\circ}$ ** Solution. ** \begin{align*} & \quad \sin 70^{\circ}... function: $\sin 76^{\circ} - \sin 14^{\circ}$ ** Solution. ** \begin{align*} & \quad \sin 76^{\circ} ... function: $\cos 58^{\circ} + \cos 12^{\circ}$ ** Solution. ** \begin{align*} &\quad \cos 58^{\circ}
- Question 3(i, ii, iii, iv & v) Exercise 8.3
- uestion 3(i, ii, iii, iv & v) Exercise 8.3 ====== Solutions of Question 3(i, ii, iii, iv & v) of Exerci... alpha \tan \beta}{1+ \tan \alpha \tan \beta}$ ** Solution. ** \begin{align*} RHS & = \dfrac{1- \tan \... u}{\sin (-6u)}=-\dfrac{\sin 10 u}{\sin 6u}+3$ ** Solution. ** \begin{align*} RHS & = \dfrac{6 \cos 8u... ntity $4 \cos 4v \sin 3v=2(\sin 7v - \sin v)$ ** Solution. ** \begin{align*} RHS & = 4 \cos 4v \sin 3
- Question 3(vi, vii, viii, ix & x) Exercise 8.3
- tion 3(vi, vii, viii, ix & x) Exercise 8.3 ====== Solutions of Question 3(vi, vii, viii, ix & x) of Exe... ty $2\tan y \cos 3y= \sec y(\sin 4y-\sin 2y)$ ** Solution. ** \begin{align*} LHS & = 2\tan y \cos 3y ... beta - \sin 4 \beta}=\tan 5 \beta \cot \beta$ ** Solution. ** \begin{align*} LHS & = \dfrac{ \sin 6 \... \cot \theta}=-\cos 2 \theta \cot \theta$. m( ** Solution. ** \begin{align*} LHS & = \dfrac{ \cot 3 \
- Question 2, Exercise 8.1
- ====== Question 2, Exercise 8.1 ====== Solutions of Question 2 of Exercise 8.1 of Unit 08: Fundamental ... ng $\cos \left(45^{\circ}-30^{\circ}\right)$. ** Solution. ** \begin{align*} \cos 15^{\circ} & = \cos... g $\cos \left(180^{\circ}-15^{\circ}\right)$. ** Solution. ** \begin{align*} \cos 165^{\circ} & = \co... g $\cos \left(360^{\circ}-15^{\circ}\right)$. ** Solution. ** We are given that $\cos 15^\circ = \dfr
- Question 5 Exercise 8.2
- ====== Question 5 Exercise 8.2 ====== Solutions of Question 5 of Exercise 8.2 of Unit 08: Fundamental o... \sin 2 \theta=\frac{24}{25}, 2 \theta$ in QII ** Solution. ** Given: $\sin 2\theta=\dfrac{24}{25}$, $... cos 2 \theta=-\frac{7}{25}, 2 \theta$ in QIII ** Solution. ** Given: \(\cos 2\theta = -\dfrac{7}{25}\... 2 \theta=-\frac{240}{289}, 2 \theta$ in QIII ** Solution. ** Given: \(\sin 2\theta = -\dfrac{240}{28
- Question 8(xiii, xiv & xv) Exercise 8.2
- = Question 8(xiii, xiv & xv) Exercise 8.2 ====== Solutions of Question 8(xiii, xiv & xv) of Exercise 8... es: $\csc 2 \alpha-\cot 2 \alpha=\tan \alpha$ ** Solution. ** \begin{align*} LHS &= \csc 2 \alpha-\co... in 3 x}{\cos x-\sin x}=\dfrac{2+\sin 2 x}{2}$ ** Solution. ** \begin{align*} LHS & = \dfrac{\cos 3 x... \alpha}-\dfrac{\cos 3 \alpha}{\cos \alpha}=2$ ** Solution. ** \begin{align*} LHS &= \dfrac{\sin 3 \al
- Question 1(v, vi, vii & viii) Exercise 8.3
- Question 1(v, vi, vii & viii) Exercise 8.3 ====== Solutions of Question 1(v, vi, vii & viii) of Exercis... e the sum or difference: $ \sin(-u) \sin 5u$. ** Solution. ** \begin{align*} &\sin(-u) \sin 5u \\ =& ... ce: $-2 \sin 100^{\circ}\sin (-20^{\circ}) $. ** Solution. ** \begin{align*} &-2 \sin 100^{\circ} \si... ifference: $\cos 23^{\circ} \sin 17^{\circ}$. ** Solution. ** \begin{align*} &\cos 23^{\circ} \sin 17
- Question 9, Exercise 8.1
- ====== Question 9, Exercise 8.1 ====== Solutions of Question 9 of Exercise 8.1 of Unit 08: Fundamental ... dfrac{3}{5}$ find: $\sin (\alpha \pm \beta)$ ** Solution. ** Given: $\sin \alpha=\dfrac{1}{\sqrt{2}}... -\frac{3}{5}$ find: $\cos (\alpha \pm \beta)$ ** Solution. ** Given: $\sin \alpha=\dfrac{1}{\sqrt{2}}... -\frac{3}{5}$ find: $\tan (\alpha \pm \beta)$ ** Solution. ** Given: $\sin \alpha=\dfrac{1}{\sqrt{2}}