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- Question, Exercise 10.1
- os \beta =-\dfrac{12}{13}$, $\alpha $in Quadrant III and $\beta $in Quadrant II, find the exact value of $\sin \left( \alpha -\beta \right)$. ====Solut... 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 valu
- Question 1, Review Exercise 10
- collapsed="true">(B): $\dfrac{1}{2}$</collapse> ii. If $\tan {{15}^{\circ }}=2-\sqrt{3}$, then the v... collapsed="true">(B): $\dfrac{1}{2}$</collapse> iii. If $\tan \left( \alpha +\beta \right)=\dfrac{1... ac{1}{2}$</collapse> vii. A point is in Quadrant-III and on the unit circle. If its x-coordinate is $
- Question 1, Exercise 10.1
- n {{59}^{\circ }}. \end{align} ===== Question 1(ii)===== Write as a trigonometric function of a sin... os {{30}^{\circ }}\end{align}. ===== Question 1(iii)===== Write as a trigonometric function of a si
- 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:$\tan {{105}^{\circ }}$ ==
- 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=\dfr
- Question 5, Exercise 10.1
- alpha +\beta)=\dfrac{33}{65}.}$$ =====Question 5(ii)===== If $\tan \alpha =\dfrac{3}{4}$, $\sec \bet... alpha +\beta)=\dfrac{16}{65}.}$$ =====Question 5(iii)===== If $\tan\alpha =\dfrac{3}{4}$, $\sec \bet
- 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}.}$$ =====Question 2(ii)===== If $\sin \theta =\dfrac{5}{13}$ and termina... s 2\theta=-\dfrac{119}{169}.}$$ =====Question 2(iii)===== If $\sin \theta =\dfrac{5}{13}$ and termi
- 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
- Question 7, Exercise 10.2
- \sec 2\theta }=R.H.S.\end{align} =====Question 7(ii)===== Prove the identity $\tan \dfrac{\theta }{2}... e\, angle\, identity)\end{align} =====Question 7(iii)===== Prove the identity $\dfrac{1+\cos 2\theta
- 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{\
- 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... frac{3}{16}=R.H.S.\end{align} =====Question 5(iii)===== Prove the identity $\sin {{10}^{\circ }}\s