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- Question 13, Exercise 10.1
- i\cos\theta\right)\\ &=r\sin(\theta+\varphi),\\ &\text{ where } \sin\varphi=\dfrac{3}{5}, \cos\varphi=\dfrac{4}{5} \text{ and } r=5.\end{align} =====Question 13(ii)=====... i\cos\theta\right)\\ &=r\sin(\theta+\varphi),\\ &\text{ where } \sin\varphi=\dfrac{8}{17}, \cos\varphi=\dfrac{15}{17} \text{ and } r=17.\end{align} =====Question 13(iii)===
- Question 5, Exercise 10.3
- circ-40^\circ) \right)\sin {{20}^{\circ }} \quad \text{by using (1)}\\ &=-\dfrac{\sqrt{3}}{4}\left( \cos... +20^\circ)-\sin(40^\circ-20^\circ) \right) \quad \text{by using (2)}\\ &=\dfrac{\sqrt{3}}{8}\sin {{20}^{... ^{\circ }}-{{10}^{\circ }} \right) \right) \quad \text{by using (1)}\\ &=-\dfrac{1}{4}\sin {{50}^{\circ ... \right)+\dfrac{1}{8}\sin {{50}^{\circ }} \quad \text{by using (2)}\\ &=-\dfrac{1}{8}\left( \sin {{130}
- Question 7, Exercise 10.2
- \right)\left( 1 \right)\\ &=\cos 2\theta \quad \text{(By using double angle identity)}\\ &=\dfrac{1}{\... &=\sin 2\theta \cos 2\alpha =R.H.S.\end{align} <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-2-p5|< Question 6]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-2-p7|Question 8, 9 >]]</btn></
- Question 2, Exercise 10.1
- rac{\sqrt{2}+\sqrt{6}}{4}\end{align} ===Go to=== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-1-p1|< Question 1]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-1-p3|Question 3 >]]</btn></text>
- Question 3, Exercise 10.1
- s \left( u+v \right)&=\frac{24}{25}\end{align} <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-1-p2|< Question 2]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-1-p4|Question 4 >]]</btn></text>
- Question, Exercise 10.1
- alpha+\beta \right)&=\dfrac{33}{56}.\end{align} <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-1-p3|< Question 3]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-1-p5|Question 5 >]]</btn></text>
- Question 5, Exercise 10.1
- d black]{\tan(\alpha +\beta)=\dfrac{33}{16}.}$$ <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-1-p4|< Question 4]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-1-p6|Question 6 >]]</btn></text>
- Question 6, Exercise 10.1
- ta -{{\cos }^{2}}\alpha \\ &=R.H.S.\end{align} <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-1-p5|< Question 5]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-1-p7|Question 7 >]]</btn></text>
- Question 7, Exercise 10.1
- tan \alpha +\tan \beta \\ &=R.H.S.\end{align} <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-1-p6|< Question 6]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-1-p8|Question 8 >]]</btn></text>
- Question 8, Exercise 10.1
- \right)}\\ &=R.H.S.\end{align} ====Go to==== <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-1-p7|< Question 7]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-1-p9|Question 9,10 >]]</btn></text>
- Question 9 and 10, Exercise 10.1
- -\sin \alpha \right)}\\ &=1=R.H.S.\end{align} <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-1-p8|< Question 8]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-1-p10|Question 11,12 >]]</btn></text>
- Question11 and 12, Exercise 10.1
- \gamma +\cot \gamma \cot \alpha =1.\end{align} <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-1-p9|< Question 9,10]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-1-p11|Question 13 >]]</btn></text>
- Question 2, Exercise 10.2
- solid black]{\tan 2\theta=-\dfrac{120}{119}}$$ <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-2-p1|< Question 1]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-2-p3|Question 3 >]]</btn></text>
- Question 3, Exercise 10.2
- \cos \dfrac{\theta }{2}=\dfrac{1}{\sqrt{5}}}$$ <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-2-p2|< Question 2]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-2-p4|Question 4 >]]</btn></text>
- Question 4 and 5, Exercise 10.2
- lid black]{\cos\dfrac{2\pi}{3}=-\dfrac{1}{2}}$$ <text align="left"><btn type="primary">[[fsc-part1-kpk:sol:unit10:ex10-2-p3|< Question 3]]</btn></text> <text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-2-p5|Question 6 >]]</btn></text>