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- Question 10, Exercise 8.1
- ====== Question 10, Exercise 8.1 ====== Solutions of Question 10 of Exercise 8.1 of Unit 08: Fundamental of Trigonometry. T... ral Textbook Board, Islamabad, Pakistan. ===== Question 10(i)===== Verify: $\sin \left(\dfrac{\pi}{2}-\a... \ & = \cos\alpha = R.H.S \end{align*} GOOD ===== Question 10(ii)===== Verify: $\cos (\pi-\alpha)=-\cos \al
- Question 11, Exercise 8.1
- ====== Question 11, Exercise 8.1 ====== Solutions of Question 11 of Exercise 8.1 of Unit 08: Fundamental of Trigonometry. T... ral Textbook Board, Islamabad, Pakistan. ===== Question 11(i)===== Show that: $\dfrac{\sin \left(180^{\ci... mbda)} \\ & = 1 = R.H.S \end{align*} GOOD ===== Question 11(ii)===== Show that: $\dfrac{\sin \left(90^{\ci
- Question 3, Exercise 8.1
- ====== Question 3, Exercise 8.1 ====== Solutions of Question 3 of Exercise 8.1 of Unit 08: Fundamental of Trigonometry. Thi... eral Textbook Board, Islamabad, Pakistan. ===== Question 3(a)===== Find the exact value of $\cos 120^{\cir... circ}\\ &= -\dfrac{1}{2}. \end{align*} GOOD ===== Question 3(b)===== Find the exact value of $\sin 120^{\cir
- Question 4, Exercise 8.1
- ====== Question 4, Exercise 8.1 ====== Solutions of Question 4 of Exercise 8.1 of Unit 08: Fundamental of Trigonometry. Thi... eral Textbook Board, Islamabad, Pakistan. ===== Question 4(i)===== Rewrite as a single expression. $\cos 6... 3\theta) \\ & = \cos 9\theta . \end{align*} ===== Question 4(ii)===== Rewrite as a single expression. $\cos
- Question 4 Exercise 8.2
- ====== Question 4 Exercise 8.2 ====== Solutions of Question 4 of Exercise 8.2 of Unit 08: Fundamental of Trigonometry. This... deral Textbook Board, Islamabad, Pakistan. =====Question 4(i)===== Find (a) $\sin 2 \theta$ (b) $\cos 2 \t... \theta}{2} = \frac{1}{2}} \end{align*} GOOD =====Question 4(ii)===== Find (a) $\sin 2 \theta$ (b) $\cos 2 \
- Question 1, Exercise 8.1
- ====== Question 1, Exercise 8.1 ====== Solutions of Question 1 of Exercise 8.1 of Unit 08: Fundamental of Trigonometry. Thi... eral Textbook Board, Islamabad, Pakistan. ===== Question 1(i)===== Find the value of $\cos (\alpha \pm \be... -60) = \tan(2(90)-60) =-\tan 60^\circ$ GOOD ===== Question 1(ii)===== Find the value of $\cos (\alpha \pm \b
- Question 6 Exercise 8.2
- ====== Question 6 Exercise 8.2 ====== Solutions of Question 6 of Exercise 8.2 of Unit 08: Fundamental of Trigonometry. This... eral Textbook Board, Islamabad, Pakistan. =====Question 6(i)===== Use a double-angle identity to find exa... ^{\circ} = \frac{1}{4}} \end{align*} GOOD =====Question 6(ii)===== Use a double-angle identity to find ex
- Question 2(i, ii, iii, iv and v) Exercise 8.3
- ====== Question 2(i, ii, iii, iv and v) Exercise 8.3 ====== Solutions of Question 2(i, ii, iii, iv and v) of Exercise 8.3 of Unit 0... deral Textbook Board, Islamabad, Pakistan. =====Question 2(i)===== Rewrite the sum or difference as a prod... 50^\circ \cos 20^\circ \end{align*} GOOD =====Question 2(ii)===== Rewrite the sum or difference as a pro
- Question 2, Exercise 8.1
- ====== Question 2, Exercise 8.1 ====== Solutions of Question 2 of Exercise 8.1 of Unit 08: Fundamental of Trigonometry. Thi... eral Textbook Board, Islamabad, Pakistan. ===== Question 2(a)===== Find the exact value of $\cos 15^{\circ... t{3}+1}{2\sqrt{2}}. \end{align*} GOOD ===== Question 2(b)===== Use the value of $\cos 15^{\circ}=\dfra
- Question 5 Exercise 8.2
- ====== Question 5 Exercise 8.2 ====== Solutions of Question 5 of Exercise 8.2 of Unit 08: Fundamental of Trigonometry. This... deral Textbook Board, Islamabad, Pakistan. =====Question 5(i)===== Find exact values for $\sin \theta$, $\... ed{\tan\theta=\frac{4}{3}} \end{align*} GOOD =====Question 5(ii)===== Find exact values for $\sin \theta, \c
- 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 8.2 of Unit 08: Fun... deral Textbook Board, Islamabad, Pakistan. =====Question 8(xiii)===== Verify the identities: $\csc 2 \alph... a}\\ &=\tan \alpha\\ &=RHS \end{align*} GOOD =====Question 8(xiv)===== Verify the identities: $\dfrac{\cos 3
- 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 Exercise 8.3 of Unit 08: ... deral Textbook Board, Islamabad, Pakistan. =====Question 1(v)===== Use the product-to-sum formula to chang... }{2}[\cos(6u) - \cos(4u) ] \end{align*} GOOD =====Question 1(vi)===== Use the product-to-sum formula to chan
- Question 9, Exercise 8.1
- ====== Question 9, Exercise 8.1 ====== Solutions of Question 9 of Exercise 8.1 of Unit 08: Fundamental of Trigonometry. Thi... eral Textbook Board, Islamabad, Pakistan. ===== Question 9(i)===== Given $\alpha$ and $\beta$ are obtuse a... }} \\ &= \frac{1}{5\sqrt{2}}. \end{align*} ===== Question 9(ii)===== Given $\alpha$ and $\beta$ are obtuse
- Question 12, Exercise 8.1
- ====== Question 12, Exercise 8.1 ====== Solutions of Question 12 of Exercise 8.1 of Unit 08: Fundamental of Trigonometry. T... ral Textbook Board, Islamabad, Pakistan. ===== Question 12(i)===== If $\alpha+\beta+\gamma=180^{\circ}$, ... \gamma \\ \end{align*} as required. GOOD ===== Question 12(ii)===== If $\alpha+\beta+\gamma=180^{\circ}$,
- Question 13, Exercise 8.1
- ====== Question 13, Exercise 8.1 ====== Solutions of Question 13 of Exercise 8.1 of Unit 08: Fundamental of Trigonometry. T... ral Textbook Board, Islamabad, Pakistan. ===== Question 13(i)===== Express in the form of $r \sin (\theta... tan^{-1}\left(-\frac{5}{12}\right)$. GOOD ===== Question 13(ii)===== Express in the form of $r \sin (\thet