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- Question 3(vi, vii, viii, ix & x) Exercise 8.3
- = \sec y(\sin 4y - \sin 2y)\\ &= RHS \end{align*} GOOD =====Questio 3(vii)===== Prove the identity $\d... & = \tan 5\beta \cot \beta\\ &= RHS \end{align*} GOOD =====Questio 3(viii)===== Prove the identity $\... ta} \\ & = -2 \cos 2\theta \\ &= RHS \end{align*} GOOD :!: **Correction:**\\ The corrected version of... \ & = \cos 7x \sec 5x \cot x\\ &=RHS \end{align*} GOOD =====Questio 3(x)===== Prove the identity $\df
- Question 2, Exercise 8.1
- \ & = \dfrac{\sqrt{3}+1}{2\sqrt{2}}. \end{align*} GOOD ===== Question 2(b)===== Use the value of... & = -\dfrac{\sqrt{3}+1}{2\sqrt{2}}. \end{align*} GOOD **Alternative Method (if $\cos 15^{\circ}$ is ... & = -\dfrac{\sqrt{3}+1}{2\sqrt{2}}. \end{align*} GOOD ===== Question 2(c)===== Use the value of $\co... rc = \frac{\sqrt{3}+1}{\sqrt{3}-1}} \end{align*} GOOD ====Go to ==== <text align="left"><btn type="p
- Question 8(xix, xx, xxi & xxii) Exercise 8.2
- cos\alpha}\\ & = \sec\alpha \\ &=RHS \end{align*} GOOD =====Question 8(xx)===== Verify the identi... \frac{\beta}{2} \\ & = 1 \\ & = RHS \end{align*} GOOD =====Question 8(xxi)===== Verify the identi... } \\ & = 2\cos y \sec 2y \\ & = LHS \end{align*} GOOD =====Question 8(xxii)===== Verify the identit... } \\ & = 2\sin y \sec 2y \\ & = LHS \end{align*} GOOD ====Go to ==== <text align="left"><
- Question 1(v, vi, vii & viii) Exercise 8.3
- =& \frac{1}{2}[\cos(6u) - \cos(4u) ] \end{align*} GOOD =====Question 1(vi)===== Use the product-to-sum... = \cos 80^{\circ} - \cos 120^{\circ} \end{align*} GOOD :!: =====Question 1(vii)===== Use the product-t... [ \sin 40^{\circ} - \sin 6^{\circ} ] \end{align*} GOOD =====Question 1(viii)===== Use the product-to-... & \sin 104^{\circ} - \sin 8^{\circ} \end{align*} GOOD ====Go to ==== <text align="left"><btn type
- Question 4, Exercise 8.1
- heta -2\theta) \\ & = \cos 5\theta . \end{align*} GOOD ===== Question 4(iii)===== Rewrite as a single ... = \sin \left(\frac{\theta}{2}\right) \end{align*} GOOD ===== Question 4(iv)===== Rewrite as a single e... 5^{\circ}) \\ & = \tan(30^{\circ}). \end{align*} GOOD ===== Question 4(vi)===== Rewrite as a single e... & = \tan\left(2\pi\right). \end{align*} ====Go to ==== <text align="left"><btn type="primary">[
- Question 10, Exercise 8.1
- sin\alpha \\ & = \cos\alpha = R.H.S \end{align*} GOOD ===== Question 10(ii)===== Verify: $\cos (\pi-... \cos \alpha-\sin \alpha)\\ & = R.H.S \end{align*} GOOD ===== Question 10(iv)===== Verify: $\sin \lef... s \gamma+\sin \gamma}{\cos \gamma-\sin \gamma}.$$ GOOD ===== Question 10(vii)===== Verify: $\cos (x+... 2 \cos x \sin y \\ & = R.H.S. \end{align*} ====Go to ==== <text align="left"><btn type="primary">[
- Question 12, Exercise 8.1
- \tan\beta\tan\gamma \\ \end{align*} as required. GOOD ===== Question 12(ii)===== If $\alpha+\beta+... }\cot \frac{\gamma }{2} \end{align*} as required. GOOD ===== Question 12(iii)===== If $\alpha+\beta+... ac{\alpha }{2}-1= 0 \\ \end{align*} as required. GOOD ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:sol:unit08:ex8-1-p10|< Que
- Question 1(i, ii, iii & iv) Exercise 8.3
- 6x-10x)]\\ &= 2[\sin (26x)+\sin(6x)] \end{align*} GOOD =====Question 1(ii)===== Use the product-to-sum... 6y) ] \\ &= 5[\cos(16y)+\cos(4y) ] \end{align*} GOOD =====Question 1(iii)===== Use the product-to-su... - 5x)] \\ &= 3[\sin(15x) - \sin(5x)] \end{align*} GOOD ====Go to ==== <text align="right"><btn type="success">[[math-11-nbf:sol:unit08:ex8-3-p2|Question
- Question 1(ix, x & xi) Exercise 8.3
- \cos 60^{\circ} - \cos 90^{\circ} \\ \end{align*} GOOD =====Question 1(x)===== Use the product-to-sum... \right)] \\ &= 2[\sin u + \sin v ] \end{align*} GOOD =====Question 1(xi)===== Use the product-to-sum... +v \right) \\ & = \sin 2u - \sin 2v \end{align*} GOOD ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:sol:unit08:ex8-3-p2|< Question
- Question 3(i, ii, iii, iv & v) Exercise 8.3
- eta)}{\cos(\alpha+\beta)} \\ & = LHS \end{align*} GOOD =====Questio 3(ii)===== Prove the identity $... 4 \cos^2 \theta \sin \theta\\ &=RHS \end{align*} GOOD =====Questio 3(v)===== Prove the identity $\co... x \\ & = 2 \cos x (\cos 2x) \\ &=RHS \end{align*} GOOD ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:sol:unit08:ex8-3-p4|< Qu
- Question 5 and 6, Review Exercise
- = 4 \\ \implies & \tan \theta = 2 \end{align*} GOOD =====Question 6(i)===== If $\sin (\alpha+\theta... frac{2-\tan \theta}{1-2 \tan \theta} \end{align*} GOOD =====Question 6(ii)===== If $\sin (\alpha-\thet... ha} = 1\\ \implies &\tan \alpha = 1 \end{align*} GOOD ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:sol:unit08:Re-ex-p4|< Question
- Question 1, Exercise 8.1
- \dfrac{-\sqrt{3}}{1+0} = -\sqrt{3} \end{align*} GOOD m( **Alternative Method** * $\cos(180+60) =... $\tan(180-60) = \tan(2(90)-60) =-\tan 60^\circ$ GOOD ===== Question 1(ii)===== Find the value of $\c... }{1 + 1} \\ & = 0 = \tan \pi \end{align*} ====Go to ==== <text align="right"><btn type="success">
- Question 3, Exercise 8.1
- \sin 30^{\circ}\\ &= -\dfrac{1}{2}. \end{align*} GOOD ===== Question 3(b)===== Find the exact value o... }\\ &= \frac{\sqrt{3}-1}{2\sqrt{2}}. \end{align*} GOOD ===== Question 3(d)===== Use the value of $\cos... sqrt{3} - 1}{2\sqrt{2}}. \end{align*} ====Go to ==== <text align="left"><btn type="primary">[
- Question 11, Exercise 8.1
- bda)(-\sin\lambda)} \\ & = 1 = R.H.S \end{align*} GOOD ===== Question 11(ii)===== Show that: $\dfrac... \cos \alpha \cos \beta} \\ & = R.H.S \end{align*} GOOD ===== Question 11(iv)===== Show that: $\sin (\... = \sin 5\theta \\ & = R.H.S \end{align*} ====Go to ==== <text align="left"><btn type="primary">[
- Question 1, 2 and 3 Exercise 8.2
- ative. This gives $2\theta$ lies in III quadrant. GOOD =====Question 2===== If $\sin \alpha=y$ and $\a... alpha=-\frac{y\sqrt{1-y^2}}{1-2y^2}} \end{align*} GOOD =====Question 3===== Use a half angle formula t... {0.134}{2}}=\sqrt{0.067}=0.259 \end{align*} ====Go to ==== <text align="right"><btn type="success">