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- Question 6, Exercise 10.2
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... {\circ }}}{2}$, we can find $\cos {{15}^{\circ }}$by using half angle identity as, \begin{align}\cos {... c }}}{2}$, so we can find $\tan {{67.5}^{\circ }}$by using half angle identity as, \begin{align}\tan {... rc }}}{2}$, so we can find $sin{{112.5}^{\circ }}$by using half angle identity as, \begin{align} sin{
- Question 2, Exercise 10.2
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... a = -\dfrac{12}{13}$$ Thus, we have the following by using double angle identities: \begin{align}\sin ... a = -\dfrac{12}{13}$$ Thus, we have the following by using double angle identities: \begin{align}\cos ... a = -\dfrac{12}{13}$$ Thus, we have the following by using double angle identities: Thus, we have the
- Question 3, Exercise 10.2
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... al ray of $\theta$ is in the second quadrant and by drawing the reference triangle as shown: {{ :fsc... eta =-\dfrac{3}{5}$. Thus, we have the following by using double angle identity: \begin{align}\sin 2\... al ray of $\theta$ is in the second quadrant and by drawing the reference triangle as shown: {{ :fsc
- Question 5, Exercise 10.3
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... 40^\circ) \right)\sin {{20}^{\circ }} \quad \text{by using (1)}\\ &=-\dfrac{\sqrt{3}}{4}\left( \cos {{... circ)-\sin(40^\circ-20^\circ) \right) \quad \text{by using (2)}\\ &=\dfrac{\sqrt{3}}{8}\sin {{20}^{\ci... rc }}-{{10}^{\circ }} \right) \right) \quad \text{by using (1)}\\ &=-\dfrac{1}{4}\sin {{50}^{\circ }}\
- Question 4 and 5, Exercise 10.2
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... s gives $\frac{\theta}{2}$ lies in 2nd quadrant. By using the half angle identity: $$\sin\dfrac{\thet... ===Solution==== Given: $\sin \dfrac{2\pi }{3}$.\\ By using double angle identities, we have \begin{ali... ===Solution==== Given: $\cos \dfrac{2\pi }{3}$ \\ By using double angle identities, we have \begin{ali
- Question 7, Exercise 10.2
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... t)\left( 1 \right)\\ &=\cos 2\theta \quad \text{(By using double angle identity)}\\ &=\dfrac{1}{\sec ... heta }{2}}\\ &=\dfrac{2}{2\sin \theta }\quad (By \,using\, double\, angle\, identity)\end{align} ... lpha }{2}}{2{{\cos }^{2}}\dfrac{\alpha }{2}}\quad(By\, using\, half\, angle\, identity\, and\, double\
- Question 1, Exercise 10.2
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... 1}{5}$, $\theta$ in quadrant II. ====Solution==== By drawing the reference triangle as shown: {{ :fsc... frac{-5}{\sqrt{26}}$ Thus, we have the following by using double angle identities. \begin{align}\sin
- Question11 and 12, Exercise 10.1
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... ta \tan \gamma. \end{align} Dividing through out by $\tan \alpha \tan \beta \tan \gamma $ to get \beg
- Question 8 and 9, Exercise 10.2
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... \theta -1}{2\sin 2\theta \cos 2\theta}\quad\text{(by using double angle identity)}\\ &=\dfrac{2{{\cos
- Question 1, Exercise 10.1
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)
- Question 2, Exercise 10.1
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)
- Question 3, Exercise 10.1
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)
- Question, Exercise 10.1
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)
- Question 5, Exercise 10.1
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)
- Question 6, Exercise 10.1
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)