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- Question 1, Exercise 1.1
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Fulltext results:
- Unit 10: Trigonometric Identities of Sum and Difference of Angles (Solutions) @fsc-part1-kpk:sol
- tions)"> * [[fsc-part1-kpk:sol:unit10:ex10-1-p1|Question 1]] * [[fsc-part1-kpk:sol:unit10:ex10-1-p2|Question 2]] * [[fsc-part1-kpk:sol:unit10:ex10-1-p3|Question 3]] * [[fsc-part1-kpk:sol:unit10:ex10-1-p4|Question 4]] * [[fsc-part1-kpk:sol:unit10:ex10-1-p5|Questi
- Unit 1: Complex Numbers (Solutions) @fsc-part1-kpk:sol
- utions)"> * [[fsc-part1-kpk:sol:unit01:ex1-1-p1|Question 1]] * [[fsc-part1-kpk:sol:unit01:ex1-1-p2|Question 2-3]] * [[fsc-part1-kpk:sol:unit01:ex1-1-p3|Question 4]] * [[fsc-part1-kpk:sol:unit01:ex1-1-p4|Question 5]] * [[fsc-part1-kpk:sol:unit01:ex1-1-p5|Question 6
- Question 7, Exercise 10.2 @fsc-part1-kpk:sol:unit10
- ====== Question 7, Exercise 10.2 ====== Solutions of Question 7 of Exercise 10.2 of Unit 10: Trigonometric Identities of Su... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 7(i)===== Prove the identity ${{\cos }^{4}}\theta... =\dfrac{1}{\sec 2\theta }=R.H.S.\end{align} =====Question 7(ii)===== Prove the identity $\tan \dfrac{\theta
- Question 7, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- ====== Question 7, Exercise 1.2 ====== Solutions of Question 7 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 7(i)===== Separate into real and imaginary parts ... {4}{29}$\\ Imaginary part $=\dfrac{19}{29}$ =====Question 7(ii)===== Separate into real and imaginary parts
- Question 1, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- ====== Question 1, Exercise 10.1 ====== Solutions of Question 1 of Exercise 10.1 of Unit 10: Trigonometric Identities of S... PTBB) Peshawar, Pakistan. There are four parts in Question 1. ===== Question 1(i) ===== Write as a trigonometric function of a single angle. $\sin {{37}^{\circ }}\co
- Question 2, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- ====== Question 2, Exercise 10.1 ====== Solutions of Question 2 of Exercise 10.1 of Unit 10: Trigonometric Identities of S... ok Board (KPTB or KPTBB) Peshawar, Pakistan. ====Question 2(i)==== Evaluate exactly: $\sin \dfrac{\pi }{12... \ &=\frac{\sqrt{6}-\sqrt{2}}{4}. \end{align} ===Question 2(ii)=== Evaluate exactly:$\tan {{75}^{\circ }}$
- Question 6, Exercise 10.2 @fsc-part1-kpk:sol:unit10
- ====== Question 6, Exercise 10.2 ====== Solutions of Question 6 of Exercise 10.2 of Unit 10: Trigonometric Identities of Su... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 6(i)===== Use the half angle identities to evalua... }=\dfrac{\sqrt{2+\sqrt{3}}}{2}\end{align} =====Question 6(ii)===== Use the half angle identities to evalu
- Question 8, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- ====== Question 8, Exercise 1.2 ====== Solutions of Question 8 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 8(i)===== Show that $z+\overline{z}=2\operatorna... operatorname{Re}\left( z \right)\end{align} =====Question 8(ii)===== Show that $z-\overline{z}=2i\operator
- Question 2 & 3, Review Exercise 1 @fsc-part1-kpk:sol:unit01
- ====== Question 2 & 3, Review Exercise 1 ====== Solutions of Question 2 & 3 of Review Exercise 1 of Unit 01: Complex Number... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 2===== Show that ${{i}^{n}}+{{i}^{n+1}}+{{i}^{n+2... i\left( 0 \right)\\ &=0=R.H.S.\end{align} =====Question 3(i)===== Express the complex number $\left( 1+3i
- Question 2 & 3, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- ====== Question 2 & 3, Exercise 1.1 ====== Solutions of Question 2 & 3 of Exercise 1.1 of Unit 01: Complex Numbers. This is... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 2===== Prove that ${{i}^{107}}+{{i}^{112}}+{{i}^{... 76}}\\ &=-i+1-1+i\\ &=0=R.H.S.\end{align} =====Question 3(i)===== Add the complex numbers $3\left( 1+2i \
- Question 6, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- ====== Question 6, Exercise 1.1 ====== Solutions of Question 6 of Exercise 1.1 of Unit 01: Complex Numbers. This is unit of... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 6(i)===== Perform the indicated division $\dfrac{... \\ &=\dfrac{1}{2}-\dfrac{1}{2}i\end{align} =====Question 6(ii)===== Perform the indicated division $\dfra
- Question 2, Exercise 1.3 @fsc-part1-kpk:sol:unit01
- ====== Question 2, Exercise 1.3 ====== Solutions of Question 2 of Exercise 1.3 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 2(i)===== Factorize the polynomial $P(z)$ into li... right]\\ &=(z+2)(z-1+3i)(z-1-3i)\end{align} =====Question 2(ii)===== Factorize the polynomial $P(z)$ into l
- Question 5, Exercise 1.3 @fsc-part1-kpk:sol:unit01
- ====== Question 5, Exercise 1.3 ====== Solutions of Question 5 of Exercise 1.3 of Unit 01: Complex Numbers. This is unit of... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 5(i)===== Find the solutions of the equation ${{z... frac{1}{2}-\dfrac{\sqrt{11}}{2}i\end{align} =====Question 5(ii)===== Find the solutions of the equation ${{
- Question 3, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- ====== Question 3, Exercise 10.1 ====== Solutions of Question 3 of Exercise 10.1 of Unit 10: Trigonometric Identities of S... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 3(i)===== If $\sin u=\dfrac{3}{5}$ and $\sin v=\d... 5}\\ \cos \left( u+v \right)&=0\end{align} =====Question 3(ii)===== If $\sin u=\dfrac{3}{5}$ and $\sin v=
- Question 8, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- ====== Question 8, Exercise 10.1 ====== Solutions of Question 8 of Exercise 10.1 of Unit 10: Trigonometric Identities of S... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 8(i)===== Prove that: $\tan \left( \dfrac{\pi }... \cos\theta -\sin\theta }=R.H.S.\end{align} =====Question 8(ii)===== Prove that: $\tan \left( \dfrac{\pi