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- Unit 10: Trigonometric Identities of Sum and Difference of Angles (Solutions)
- Question 1, Exercise 10.1
- Question 2, Exercise 10.1
- Question 3, Exercise 10.1
- Question, Exercise 10.1
- Question 5, Exercise 10.1
- Question 6, Exercise 10.1
- Question 7, Exercise 10.1
- Question 8, Exercise 10.1
- Question 9 and 10, Exercise 10.1
- Question11 and 12, Exercise 10.1
- Question 13, Exercise 10.1
- Question 1, Exercise 10.2
- Question 2, Exercise 10.2
- Question 3, Exercise 10.2
- Question 4 and 5, Exercise 10.2
- Question 6, Exercise 10.2
- Question 7, Exercise 10.2
- Question 8 and 9, Exercise 10.2
- Question 1, Exercise 10.3
- Question 2, Exercise 10.3
- Question 3, Exercise 10.3
- Question 5, Exercise 10.3
- Question 5, Exercise 10.3
- Question 1, Review Exercise 10
- Question 2 and 3, Review Exercise 10
- Question 4 & 5, Review Exercise 10
- Question 6 & 7, Review Exercise 10
- Question 8 & 9, Review Exercise 10
Fulltext results:
- Question 5, Exercise 10.3 @fsc-part1-kpk:sol:unit10
- ====== Question 5, Exercise 10.3 ====== Solutions of Question 5 of Exercise 10.3 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of... ==Question 5(iii)===== Prove the identity $\sin {{10}^{\circ }}\sin {{30}^{\circ }}\sin {{50}^{\circ }
- Question 5, Exercise 10.3 @fsc-part1-kpk:sol:unit10
- ====== Question 5, Exercise 10.3 ====== Solutions of Question 5 of Exercise 10.3 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of... ==Question 5(iii)===== Prove the identity $\sin {{10}^{\circ }}\sin {{30}^{\circ }}\sin {{50}^{\circ }
- Question 2 and 3, Review Exercise 10 @fsc-part1-kpk:sol:unit10
- ====== Question 2 and 3, Review Exercise 10 ====== Solutions of Question 2 and 3 of Review Exercise 10 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of M... ==Question 3===== Prove the identity $\dfrac{\sin 10a-\sin 4a}{\sin 4a+\sin 2a}=\dfrac{\cos 7a}{\cos a
- Unit 10: Trigonometric Identities of Sum and Difference of Angles (Solutions) @fsc-part1-kpk:sol
- ===== Unit 10: Trigonometric Identities of Sum and Difference of Angles (Solutions) ===== This is a t... <accordion><panel type="default" title="Exercise 10.1 (Solutions)"> * [[fsc-part1-kpk:sol:unit10:ex... * [[fsc-part1-kpk:sol:unit10:ex10-1-p9|Question 9-10]] * [[fsc-part1-kpk:sol:unit10:ex10-1-p10|Quest... ]] </panel> <panel type="default" title="Exercise 10.2 (Solutions)"> * [[fsc-part1-kpk:sol:unit10:
- Question 2, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- 2 z_3&=(3-2i)\cdot(2-2i)\\ &=(6-4)+(-4-6)i\\ &=2-10i \end{align} So \begin{align} z_1(z_2 z_3)&=(-1+i)\cdot (2-10i)\\ &=(-2+10)+(2+10)i\\ &=8+12i \ldots (3)\end{align} Now, we take \begin{align} z_1 z_2 &=(-1+i)\cdot (3-2i)\\ &
- Question 2, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- ====== Question 2, Exercise 10.1 ====== Solutions of Question 2 of Exercise 10.1 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of... ===Question 2(iii)=== Evaluate exactly:$\tan {{105}^{\circ }}$ ==Solution== We rewrite ${{105}^{{}^
- Question 9 and 10, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- ====== Question 9 and 10, Exercise 10.1 ====== Solutions of Question 9 and 10 of Exercise 10.1 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit o
- Question 8, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- ight)i}{16+49}\\ &=\dfrac{50-120i}{65}\\ &=\dfrac{10-24i}{13}\\ &=\dfrac{10}{13}-\dfrac{24i}{13}\end{align} =====Question 8(ii)===== Express the $\dfrac{... 4i}\times \dfrac{-5+4i}{-5+4i}\\ &=\dfrac{\left( -10-12 \right)+\left( 8-15 \right)i}{25+16}\\ &=\dfra... ign="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:ex1-1-p8|Question 9 & 10 >]]</btn></text>
- 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 Sum and Difference of Angles. This is unit of A Textbook of... align="right"><btn type="success">[[fsc-part1-kpk:sol:unit10:ex10-1-p9|Question 9,10 >]]</btn></text>
- Question11 and 12, Exercise 10.1 @fsc-part1-kpk:sol:unit10
- ====== Question11 and 12, Exercise 10.1 ====== Solutions of Question 11 and 12 of Exercise 10.1 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of... [[fsc-part1-kpk:sol:unit10:ex10-1-p9|< Question 9,10]]</btn></text> <text align="right"><btn type="suc
- Question 1, Exercise 10.2 @fsc-part1-kpk:sol:unit10
- ====== Question 1, Exercise 10.2 ====== Solutions of Question 1 of Exercise 10.2 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of... )\left( \dfrac{-5}{\sqrt{26}} \right)\\ &=-\dfrac{10}{26} \end{align} $$ \implies \bbox[4px,border:2p
- Question 3, Exercise 10.2 @fsc-part1-kpk:sol:unit10
- ====== Question 3, Exercise 10.2 ====== Solutions of Question 3 of Exercise 10.2 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of... =\sqrt{\dfrac{1-\dfrac{3}{5}}{2}}=\sqrt{\dfrac{2}{10}}\end{align} $$\implies \bbox[4px,border:2px soli
- Question 2 & 3, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- Pakistan. =====Question 2===== Prove that ${{i}^{107}}+{{i}^{112}}+{{i}^{122}}+{{i}^{153}}=0$. ====Solution==== \begin{align}L.H.S.&={{i}^{107}}+{{i}^{112}}+{{i}^{122}}+{{i}^{153}}\\ &=i\cdot i^{106}+i^{112}+i^{122}+i\cdot i^{152}\\ &=i.{{\left( {
- Question 9 & 10, Exercise 1.1 @fsc-part1-kpk:sol:unit01
- ====== Question 9 & 10, Exercise 1.1 ====== Solutions of Question 9 & 10 of Exercise 1.1 of Unit 01: Complex Numbers. This i... 3}{25}+\dfrac{16}{25}i\end{align} =====Question 10===== Evalute ${{\left[ {{i}^{18}}+{{\left( \dfr
- Question 7, Exercise 1.2 @fsc-part1-kpk:sol:unit01
- }{5+2i} \quad \text{by rationalizing} \\ =&\dfrac{10-6+15i+4i}{25+4}\\ =&\dfrac{4+19i}{29}\\ =&\dfrac{... \\ =&\dfrac{-3-12+4i-9i}{1+9}\\ =&\dfrac{-15-5i}{10}\\ =&\dfrac{-3}{2}-\dfrac{1}{2}i\end{align} Rea... mes \dfrac{-5-12i}{-5-12i}\\ =&\dfrac{45-480+200i+108i}{25+144}\\ =&\dfrac{-435+308i}{169}\\ =&\dfrac{