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- Question, Exercise 10.1
- $\alpha $in Quadrant III and $\beta $in Quadrant II, find the exact value of $\sin \left( \alpha -\be... ght)&=\frac{33}{65}.\end{align} =====Question 4(ii)===== If $\sin \alpha =-\dfrac{4}{5}$ and $\cos \... $\alpha $in Quadrant III and $\beta $in Quadrant II, find the exact value of $\cos \left( \alpha +\be... $\alpha $in Quadrant III and $\beta $in Quadrant II, find the exact value of $\tan \left( \alpha +\b
- Question 1, Exercise 10.1
- n {{59}^{\circ }}. \end{align} ===== Question 1(ii)===== Write as a trigonometric function of a sin
- Question 2, Exercise 10.1
- sqrt{6}-\sqrt{2}}{4}. \end{align} ===Question 2(ii)=== Evaluate exactly:$\tan {{75}^{\circ }}$ ==So
- 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
- Question 5, Exercise 10.1
- alpha +\beta)=\dfrac{33}{65}.}$$ =====Question 5(ii)===== If $\tan \alpha =\dfrac{3}{4}$, $\sec \bet
- Question 6, Exercise 10.1
- dfrac{\alpha }{2}$$ as required. =====Question 6(ii)===== Show that: $\sin \left( \alpha +\beta \ri
- Question 7, Exercise 10.1
- \beta \,}\\ &= R.H.S.\end{align} =====Question 7(ii)===== Show that: $\dfrac{\sin \left( \alpha +\
- Question 8, Exercise 10.1
- -\sin\theta }=R.H.S.\end{align} =====Question 8(ii)===== Prove that: $\tan \left( \dfrac{\pi }{4}-
- Question 13, Exercise 10.1
- 5} \text{ and } r=5.\end{align} =====Question 13(ii)===== Express each of the following in the form $
- Question 1, Exercise 10.2
- \tan \theta =-\dfrac{1}{5}$, $\theta$ in quadrant II. ====Solution==== By drawing the reference triang
- Question 2, Exercise 10.2
- n 2\theta=-\dfrac{120}{169}.}$$ =====Question 2(ii)===== If $\sin \theta =\dfrac{5}{13}$ and termina
- Question 3, Exercise 10.2
- \sin 2\theta=-\dfrac{24}{25}.}$$ =====Question 3(ii)===== If $\sin \theta =\dfrac{4}{5}$ and terminal
- Question 4 and 5, Exercise 10.2
- pi}{3}={\dfrac{\sqrt{3}}{2}}}$$ =====Question 5(ii)===== Use the double angle identities to evaluate
- Question 6, Exercise 10.2
- qrt{2+\sqrt{3}}}{2}\end{align} =====Question 6(ii)===== Use the half angle identities to evaluate e
- Question 7, Exercise 10.2
- \sec 2\theta }=R.H.S.\end{align} =====Question 7(ii)===== Prove the identity $\tan \dfrac{\theta }{2}