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- Question, Exercise 10.1
- s \beta =-\dfrac{12}{13}$, $\alpha $in Quadrant III and $\beta $in Quadrant II, find the exact value of $\sin \left( \alpha -\beta \right)$. ====Soluti... ght)&=\frac{33}{65}.\end{align} =====Question 4(ii)===== If $\sin \alpha =-\dfrac{4}{5}$ and $\cos \beta =-\dfrac{12}{13}$, $\alpha $in Quadrant III and $\beta $in Quadrant II, find the exact value
- Question 7, Exercise 10.2
- \sec 2\theta }=R.H.S.\end{align} =====Question 7(ii)===== Prove the identity $\tan \dfrac{\theta }{2}... \, angle\, identity)\end{align} =====Question 7(iii)===== Prove the identity $\dfrac{1+\cos 2\theta }... t 2\theta =R.H.S.\end{align} =====Question 7(vii)===== Prove the identity $\dfrac{{{\cos }^{3}}\th... \theta }{2}=R.H.S.\end{align} =====Question 7(viii)===== Prove the identity $\dfrac{2{{\cos }^{3}}\t
- Question 1, Review Exercise 10
- collapsed="true">(B): $\dfrac{1}{2}$</collapse> ii. If$\tan {{15}^{\circ }}=2-\sqrt{3}$, then the va... collapsed="true">(B): $\dfrac{1}{2}$</collapse> iii. If$\tan \left( \alpha +\beta \right)=\dfrac{1}{... collapsed="true">(B): $\dfrac{1}{2}$</collapse> vii. A point is in Quadrant-III and on the unit circle. If its x-coordinate is $-\dfrac{4}{5},$ what is t
- Question 1, Exercise 10.1
- n {{59}^{\circ }}. \end{align} ===== Question 1(ii)===== Write as a trigonometric function of a sin... s {{30}^{\circ }}\end{align}. ===== Question 1(iii)===== Write as a trigonometric function of a sin
- Question 2, Exercise 10.1
- sqrt{6}-\sqrt{2}}{4}. \end{align} ===Question 2(ii)=== Evaluate exactly:$\tan {{75}^{\circ }}$ ==So... left( \sqrt{3} \right)\end{align} ===Question 2(iii)=== Evaluate exactly:$\tan {{105}^{\circ }}$ ==S
- Question 3, Exercise 10.1
- left( u+v \right)&=0\end{align} =====Question 3(ii)===== If $\sin u=\dfrac{3}{5}$ and $\sin v=\dfra... \\ &=\dfrac{-7}{24}\end{align} =====Question 3(iii)===== If $\sin u=\dfrac{3}{5}$ and $\sin v=\dfra
- Question 5, Exercise 10.1
- alpha +\beta)=\dfrac{33}{65}.}$$ =====Question 5(ii)===== If $\tan \alpha =\dfrac{3}{4}$, $\sec \bet... lpha +\beta)=\dfrac{16}{65}.}$$ =====Question 5(iii)===== If $\tan\alpha =\dfrac{3}{4}$, $\sec \beta
- Question 8, Exercise 10.1
- -\sin\theta }=R.H.S.\end{align} =====Question 8(ii)===== Prove that: $\tan \left( \dfrac{\pi }{4}-... \right)}\\ &=R.H.S.\end{align} =====Question 8(iii)===== Prove that: $\dfrac{\tan \left( \alpha +\
- Question 13, Exercise 10.1
- 5} \text{ and } r=5.\end{align} =====Question 13(ii)===== Express each of the following in the form $... \text{ and } r=17.\end{align} =====Question 13(iii)===== Express each of the following in the form $
- Question 2, Exercise 10.2
- n 2\theta=-\dfrac{120}{169}.}$$ =====Question 2(ii)===== If $\sin \theta =\dfrac{5}{13}$ and termina... 2\theta=-\dfrac{119}{169}.}$$ =====Question 2(iii)===== If $\sin \theta =\dfrac{5}{13}$ and termin
- Question 6, Exercise 10.2
- qrt{2+\sqrt{3}}}{2}\end{align} =====Question 6(ii)===== Use the half angle identities to evaluate e... sqrt{3+2\sqrt{2}}\end{align} =====Question 6(iii)===== Use the half angle identities to evaluate e
- Question 8 and 9, Exercise 10.2
- n \theta \\ & = R.H.S\end{align} =====Question 9(ii)===== Prove the identity $\cot 4\theta =\dfrac{1-... tan 2\theta }=R.H.S.\end{align} =====Question 9(iii)===== Prove the identity $\cot 3\theta =\dfrac{\c
- Question 1, Exercise 10.3
- \theta -\cos 7\theta\end{align} =====Question 1(ii)===== Express the product as sum or difference $\... ^{\circ }} \right]. \end{align} =====Question 1(iii)===== Express the product as sum or difference: $
- Question 2, Exercise 10.3
- \circ }}\cos {{3}^{\circ }}.$$ =====Question 2(ii)===== Convert the sum or difference as product $\... =2\sin 59^\circ \sin23^\circ.$$ =====Question 2(iii)===== Convert the sum or difference as product: $
- Question 5, Exercise 10.3
- dfrac{1}{16}=R.H.S.\end{align} =====Question 5(ii)===== Prove the identity $$\sin \dfrac{\pi }{9}\s... rac{3}{16}=R.H.S.\end{align} =====Question 5(iii)===== Prove the identity $\sin {{10}^{\circ }}\si