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- Question 10, Exercise 8.1
- ft(\dfrac{\pi}{2}-\alpha\right)=\cos \alpha$ ** Solution. ** \begin{align*} L.H.S & = \sin \left(\frac{\p... === Verify: $\cos (\pi-\alpha)=-\cos \alpha$ ** Solution. ** \begin{align*} L.H.S & = \cos(\pi - \alpha) ... frac{1}{\sqrt{2}}(\cos \alpha-\sin \alpha)$ ** Solution. ** \begin{align*} L.H.S &= \cos \left(\alpha+\f... =\frac{\sqrt{2}}{2}(\cos \beta+\sin \beta)$ ** Solution. ** \begin{align*} L.H.S & = \cos \left(\alpha +
- Question 11, Exercise 8.1
- ht) \cos \left(270^{\circ}-\lambda\right)}=1$ ** Solution. ** \begin{align*} L.H.S & = \dfrac{\sin \left(1... ght)+\cos \left(90^{\circ}+\alpha\right)}=-1$ ** Solution. ** \begin{align*} L.H.S & = \frac{\sin \left(90... \sin (\alpha+\beta)}{\cos \alpha \cos \beta}$ ** Solution. ** \begin{align*} L.H.S & = \tan \alpha+\tan \b... ^{2} \alpha=\sin ^{2} \alpha-\sin ^{2} \beta$ ** Solution. ** \begin{align*} L.H.S & = \sin (\alpha + \bet
- Question 1, Exercise 8.1
- ngles. $\alpha=180^{\circ}, \beta=60^{\circ}$ ** Solution. ** Given: $\alpha=180^{\circ}$, $\beta=60^{\cir... angles. $\alpha=60^{\circ}, \beta=90^{\circ}$ ** Solution. ** Given: \(\alpha = 60^\circ\), \(\beta = 90^\... ngles. $\alpha=180^{\circ}, \beta=30^{\circ}$ ** Solution. ** Given: $\alpha = 180^\circ$, $\beta = 30^\ci... f angles. $\alpha=\pi, \beta=\frac{2 \pi}{3}$ ** Solution. ** Given: $\alpha = \pi$, $\beta = \frac{2\pi}{
- Question 3, Exercise 8.1
- nd $\cos \left(90^{\circ}+30^{\circ}\right)$. ** Solution. ** \begin{align*} \cos 120^{\circ} & = \cos \le... sin 120^{\circ}$ and then $\tan 120^{\circ}$. ** Solution. ** \begin{align*} \sin 120^{\circ} & = \sin \le... g $\cos \left(120^{\circ}-45^{\circ}\right)$. ** Solution. ** \begin{align*} \cos 75^{\circ} & = \cos \lef... g $\cos \left(180^{\circ}-75^{\circ}\right)$. ** Solution. ** \begin{align*} \cos 105^\circ & = \cos(180^\
- Question 4, Exercise 8.1
- ta \cos 3 \theta-\sin 6 \theta \sin 3 \theta$ ** Solution. ** \begin{align*} & \cos 6 \theta \cos 3 \theta... a \cos 2 \theta+\sin 7 \theta \sin 2 \theta$. ** Solution. ** \begin{align*} & \cos 7 \theta \cos 2 \theta... 3}\right) \sin \left(\frac{\theta}{6}\right)$ ** Solution. ** \begin{align*} & \sin \left(\frac{\theta}{3}... 46^{\circ}-\cos 138^{\circ} \sin 46^{\circ}$. ** Solution. ** \begin{align*} & \sin 138^{\circ} \cos 46^{\
- Question 4 Exercise 8.2
- a=\frac{3}{5}$ where $0<\theta<\frac{\pi}{2}$ ** Solution. ** Given: $\cos\theta=\dfrac{3}{5}$ where $0<\t... ac{12}{5}$ where $\pi<\theta<\frac{3 \pi}{2}$ ** Solution. ** Given: \(\tan \theta = \frac{12}{5}\) where ... {7}{25}$ where $\frac{3 \pi}{2}<\theta<2 \pi$ ** Solution. ** Given: \(\sin \theta = -\frac{7}{25}\) where... sqrt{5}$ where $\frac{3 \pi}{2}<\theta<2 \pi$ ** Solution. ** Given: \(\sec \theta = \sqrt{5}\) where \(\f
- Question 6 Exercise 8.2
- expression: $\sin 15^{\circ} \cos 15^{\circ}$ ** Solution. ** We have double-angle identity: $$\sin 2 \the... : $\cos ^{2} 15^{\circ}-\sin ^{2} 15^{\circ}$ ** Solution. ** We have double-angle identity: $$\cos^2\thet... on: $1-2 \sin ^{2}\left(\frac{\pi}{8}\right)$ ** Solution. ** We have a double-angle identity: $$\cos 2\alp... n: $2 \cos ^{2}\left(\frac{\pi}{12}\right)-1$ ** Solution. ** We have a double-angle identity: $$\cos 2\al
- Question 2(i, ii, iii, iv and v) Exercise 8.3
- function: $\sin 70^{\circ} + \sin 30^{\circ}$ ** Solution. ** \begin{align*} & \quad \sin 70^{\circ} + \s... function: $\sin 76^{\circ} - \sin 14^{\circ}$ ** Solution. ** \begin{align*} & \quad \sin 76^{\circ} - \si... function: $\cos 58^{\circ} + \cos 12^{\circ}$ ** Solution. ** \begin{align*} &\quad \cos 58^{\circ} + \co... on: $\cos \frac{p-q}{2} + \cos \frac{p+q}{2}$ ** Solution. ** \begin{align*} &\quad \cos \frac{p-q}{2} +
- Question 3(i, ii, iii, iv & v) Exercise 8.3
- alpha \tan \beta}{1+ \tan \alpha \tan \beta}$ ** Solution. ** \begin{align*} RHS & = \dfrac{1- \tan \alpha... u}{\sin (-6u)}=-\dfrac{\sin 10 u}{\sin 6u}+3$ ** Solution. ** \begin{align*} RHS & = \dfrac{6 \cos 8u \sin... ntity $4 \cos 4v \sin 3v=2(\sin 7v - \sin v)$ ** Solution. ** \begin{align*} RHS & = 4 \cos 4v \sin 3v \\ ... a + \sin \theta = 4\cos^2 \theta \sin \theta$ ** Solution. ** \begin{align*} LHS & = \sin 3 \theta + \sin
- Question 3(vi, vii, viii, ix & x) Exercise 8.3
- 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 \beta ... \cot \theta}=-\cos 2 \theta \cot \theta$. m( ** Solution. ** \begin{align*} LHS & = \dfrac{ \cot 3 \theta... \cos8x}{\sin6x-\sin4x}=\cot x \cos7x \sec 5x$ ** Solution. ** \begin{align*} LHS & = \dfrac{\cos 6x + \cos
- Question 2, Exercise 8.1
- ng $\cos \left(45^{\circ}-30^{\circ}\right)$. ** Solution. ** \begin{align*} \cos 15^{\circ} & = \cos \lef... g $\cos \left(180^{\circ}-15^{\circ}\right)$. ** Solution. ** \begin{align*} \cos 165^{\circ} & = \cos \le... g $\cos \left(360^{\circ}-15^{\circ}\right)$. ** Solution. ** We are given that $\cos 15^\circ = \dfrac{\s... 75^{\circ}$ and then find $\tan 75^{\circ}$. ** Solution. ** Given $$\cos A=\sin \left(90^{\circ}-A\right
- Question 5 Exercise 8.2
- \sin 2 \theta=\frac{24}{25}, 2 \theta$ in QII ** Solution. ** Given: $\sin 2\theta=\dfrac{24}{25}$, $2\the... cos 2 \theta=-\frac{7}{25}, 2 \theta$ in QIII ** Solution. ** Given: \(\cos 2\theta = -\dfrac{7}{25}\) and... 2 \theta=-\frac{240}{289}, 2 \theta$ in QIII ** Solution. ** Given: \(\sin 2\theta = -\dfrac{240}{289}\) ... os 2 \theta=\frac{120}{169}, 2 \theta$ in QIV ** Solution. ** Given: \(\cos 2\theta = \frac{120}{169}\) an
- Question 8(xix, xx, xxi & xxii) Exercise 8.2
- rac{\cos 2 \alpha}{\cos \alpha}=\sec \alpha$$ ** Solution. ** \begin{align*} LHS &= \dfrac{\sin 2 \alpha}{... y: $2 \sin ^{2} \frac{\beta}{2}+\cos \beta=1$ ** Solution. ** \begin{align*} LHS & = 2 \sin ^{2} \frac{\be... c{1}{\cos y-\sin y}+\frac{1}{\cos y+\sin y}$$ ** Solution. ** \begin{align*} RHS & = \frac{1}{\cos y-\sin ... c{1}{\cos y-\sin y}-\frac{1}{\cos y+\sin y}$$ ** Solution. ** \begin{align*} RHS & = \frac{1}{\cos y-\sin
- Question 1(i, ii, iii & iv) Exercise 8.3
- sum or difference: $$4 \sin 16x \cos 10x $$ ** Solution. ** \begin{align*} &4 \sin 16x \cos 10x \\ & = 2... the sum or difference: $10 \cos 10y \cos 6y$. ** Solution. ** \begin{align*} &10 \cos 10y \cos 6y \\ &= 5(... ge the sum or difference: $2 \cos5t \sin 3t$. ** Solution. ** \begin{document} \begin{align*} &2 \cos 5t \... e the sum or difference: $6\cos 5x \sin 10x$. ** Solution. ** \begin{align*} &6 \cos 5x \sin 10x \\ &= 3(2
- Question 1(v, vi, vii & viii) Exercise 8.3
- e the sum or difference: $ \sin(-u) \sin 5u$. ** Solution. ** \begin{align*} &\sin(-u) \sin 5u \\ =& -\sin... ce: $-2 \sin 100^{\circ}\sin (-20^{\circ}) $. ** Solution. ** \begin{align*} &-2 \sin 100^{\circ} \sin (-2... ifference: $\cos 23^{\circ} \sin 17^{\circ}$. ** Solution. ** \begin{align*} &\cos 23^{\circ} \sin 17^{\ci... ifference: $2 \cos56^{\circ} \sin48^{\circ}$. ** Solution. ** \begin{align*} &2 \cos 56^{\circ} \sin 48^{\